AS 3857—1999
Australian Standard™
Heat exchangers— Tubeplates—
Method of design
This Australian Standard was prepared by Committee ME/1, Pressure Equipment. It
was approved on behalf of the Council of Standards Australia on 16 April 1999 and
published on 5 July 1999.
The following interests are represented on Committee ME/1:
A.C.T. WorkCover
Australasian Corrosion Association
Australasian Institute of Engineer Surveyor
Australian Aluminium Council
Australian Building Codes Board
Australian Chamber of Commerce and Industry
Australian Industry Group
Australian Institute of Energy
Australian Institute of Petroleum
Boiler and Pressure Vessel Manufacturers Association of Australia
Bureau of Steel Manufacturers of Australia
Department for Administration and Information Services, S.A.
Department of Employment Training and Industrial Relations, Qld
Department of Industries and Business, N.T.
Department of Infrastructure, Energy and Resources (Tasmania)
Department of Labour, New Zealand
Electricity Corporation of New Zealand
Electricity Supply Association of Australia
Institute of Materials Engineering Australasia
Institution of Engineers, Australia
Institution of Professional Engineers, New Zealand
National Association of Testing Authorities, Australia
New Zealand Engineering Federation
New Zealand Heavy Engineering Research Association
New Zealand Institute of Welding
New Zealand Petrochemical Users Group
Victorian WorkCover Authority
Welding Technology Institute of Australia
WorkCover N.S.W.
WorkSafe Western Australia
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This Standard was issued in draft form for comment as DR 99023.
AS 3857—1999
Australian Standard™
Heat exchangers— Tubeplates—
Method of design
Originated as AS 3857 — 1990.
Second edition 1999.
Published by Standards Australia
(Standards Association of Australia)
1 The Crescent, Homebush, NSW 2140
ISBN 0 7337 2689 5
AS 3857 — 1999
2
PREFACE
This Standard was prepared by the Joint Standards Australia/Standards New Zealand
Committee ME/1, Pressure Equipment, to supersede AS 3857 — 1990, Heat
exchangers — Tubeplates — Method of design. Acknowledgment is gratefully made of the
considerable assistance provided by Orica Engineering Pty Ltd (formerly ICI Australia
Engineering Pty Ltd) which developed this method of design.
This Standard is the result of a consensus among representatives on the Joint Committee
to produce it as an Australian Standard. Consensus means general agreement by all
interested parties. Consensus includes an attempt to remove all objection and implies
much more than the concept of a simple majority, but not necessarily unanimity. It is
consistent with this meaning that a member may be included in the Committee list and yet
not be in full agreement with all clauses of this Standard.
The main change in this revision is the incorporation of Amendment No. 1 to
AS 3857 — 1990.
The Standard covers a method for the design of heat exchanger tubeplates. The Standard
was originally drafted with the intention that it would be incorporated into AS 1210,
Pressure vessels, as a replacement for the method contained in the first and second
editions of AS 1210 but the draft was subsequently terminated. However, during the
course of development of the proposal, its content was extended and it is now a
self-contained method of design, suitable for publication as a separate Standard.
The Standard provides an additional method to other methods specified in AS 1210 for
the design of tubeplates for heat exchangers complying with that Standard. The method
may also be suitable for the design of some boiler tubeplates.
Although the design method may appear to be somewhat complex, it is no more so than
some design methods for other pressure vessel components such as flanges.
While the method is applicable to long-hand calculations, its most effective use will be
achieved by programming a computer. An appendix provides a simple algorithm for
calculating Lord Kelvin’s modified Bessel functions and this algorithm allows programs
to be compiled on a computer. Tabulated values of the functions are also provided in the
appendix. Suggested worksheets and worked examples of calculations are included in
another appendix.
As the proposed design method allows actual stresses at any location to be determined, it
can be used for heat exchangers designed to AS 1210 Supplement 1, Unfired Pressure
vessels — Advanced design and construction (Supplement to AS 1210 — 1997).
The theoretical background for the method given in this Standard is given in a technical
paper titled ‘Australian Tubesheet Code’ by P McGowan and I Mirovics presented at the
ASME Conference on Pressure Vessels and Piping at Nashville, Tennesee in June 1990.
The terms ‘normative’ and ‘informative’ have been used in this Standard to define the
application of the appendix to which they apply. A ‘normative’ appendix is an integral
part of a Standard, whereas an ‘informative’ appendix is only for information and
guidance.
3
AS 3857 — 1999
CONTENTS
Page
1
2
3
4
5
SCOPE . . . . . . . . . . . . . . . . . . . .
APPLICATION . . . . . . . . . . . . . . .
REFERENCED DOCUMENTS . . . .
MATERIALS AND COMPONENTS
DESIGN . . . . . . . . . . . . . . . . . . .
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4
4
4
4
9
APPENDICES
A TUBE-TO-TUBEPLATE JOINT—DETERMINATION OF AXIAL
BREAKING LOAD AND JOINT EFFICIENCY . . . . . . . . . . . . . . . . . . . . . . 23
B LORD KELVIN’S MODIFIED BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . 25
C SAMPLE CALCULATION SHEETS AND WORKED EXAMPLES . . . . . . . . 31
© Copyright
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AS 3857 — 1999
4
STANDARDS AUSTRALIA
Australian Standard
Heat exchangers — Tubeplates — Method of design
1 SCOPE This Standard sets out a method for designing flat, circular tubeplates of the
following configurations:
(a)
Fixed tubeplates as in heat exchangers consisting of two tubeplates clamped or
welded to a shell between them, with or without an expansion joint in the shell.
(b)
Tubeplates of U-tube or bayonet heat exchangers.
(c)
Floating tubeplates.
Such tubeplates are used in shell-and-tube heat exchangers and in some types of boilers
including fire-tube and waste heat boilers.
2 APPLICATION This Standard is intended for use in association with an appropriate
pressure vessel or boiler Standard such as —
(a)
shell-and-tube heat exchangers
(b)
boilers
. . . . . . . . . . . AS 1210 or AS 1210 Supplement 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . AS 1228.
Calculated and permissible stresses in the tubeplates, tubes and shell shall be determined
from this Standard but all other design criteria specified in the relevant pressure vessel or
boiler Standard shall apply.
In the application of this Standard it will also be necessary to determine metal temperature
from other sources (see Clause 5.1).
3 REFERENCED DOCUMENTS
Standard:
AS
1210
1210 Supplement 1
1228
EJMA
The following documents are referred to in this
Pressure vessels
Unfired pressure vessels — Advanced design and construction
(Supplement to AS 1210 — 1997)
Pressure equipment — Boilers
Standards of the Expansion Joint Manufacturers Association, Inc.
4 MATERIALS AND COMPONENTS
4.1 Acceptable materials Materials for tubeplates and associated components shall
comply with a material specification listed, or as otherwise permitted, in AS 1210,
AS 1210 Supplement 1 or AS 1228, as appropriate.
4.2 Design strength The material design strengths, used in the analysis of the
tubeplate, shall comply with the values specified, or as otherwise permitted, in AS 1210,
AS 1210 Supplement 1 or AS 1228, as appropriate.
4.3 Coefficient of thermal expansion The values which shall be used for the mean
coefficient of thermal expansion are given in Table 4.3.
4.4 Young modulus (modulus of elasticity) The values which shall be used for Young
Modulus are given in Table 4.4.
4.5 Expansion joints Metallic expansion joints should comply with the requirements
specified in the ‘Standards of the Expansion Joint Manufacturers Associations, Inc.’ or
equivalent.
COPYRIGHT
5
AS 3857—1999
TABLE 4.3
MEAN COEFFICIENT OF THERMAL EXPANSION BETWEEN 25°C AND DESIGN TEMPERATURE
Mean coefficient of thermal expansion between 25°C and temperature, K–1 × 10–6 (µm/m.K)
Material
Design temperature, °C
–50
0
50
100
150
200
250
300
350
400
450







11.15
11.45
11.75
12.07
12.39
12.69
12.99
13.29
13.57
13.84
14.09
14.34
C–Si, C–.5Mo, .5Cr–.5Ni–.2Mo, .5Cr–.5Mo, 

.5Cr–.2Mo–V, 1Cr–.5Mo–1Cr–.2Mo,

1Cr–.2Mo–Si, 1.75Cr–.2Mo–Cu
9.29
9.89
10.49
11.08
11.63
12.14
12.60
13.02
13.40
13.74
14.02
14.27
8.96
9.56
10.16
10.77
11.34
11.86
12.34
12.77
13.16
13.51
13.82
14.08
12.37
12.60
12.83
13.09
13.34
13.58
13.80
14.01
14.20
14.38
14.55
14.70
10.74
11.10
11.46
11.86
12.21
12.54
12.83
13.11
13.36
13.60
13.82
14.01
2.25Cr–1Mo
5Cr–.5Mo, (+Si, +Ti)
7Cr–.5Mo, 7Cr–1Mo
Mn–V
5Ni–.25Mo
8Ni, 9Ni
11.13
11.34
10.18
11.39
10.59
9.25
11.50
11.60
10.40
11.80
11.00
9.75
11.87
11.85
10.62
12.21
11.41
10.25
12.15
12.05
10.83
12.55
11.74
10.72
12.46
12.24
11.04
12.88
12.03
11.09
12.75
12.41
11.24
13.18
12.29
11.39
13.01
12.59
11.43
13.45
12.55
11.66
13.24
12.75
11.62
13.70
12.78
11.90
13.46
12.91
11.80
13.93
13.01
12.12
13.64
13.06
11.97
14.14
13.23
12.31
13.82
13.21
12.14
14.33
13.44
12.48
13.98
13.35
12.29
14.51
13.64
12.63
405, 410
429, 430
304
316, 317
321
347 and 348
309, 310
S31803, 2304
N08904
12Cr–Al, 13Cr
15Cr, 17Cr
18Cr–8Ni
16Cr–12Ni–2Mo, 18Cr–13Ni–3Mo
18Cr–10Ni–Ti
18Cr–10Ni–Nb
23Cr–12Ni, 25Cr–12Ni, 25Cr–20Ni
22Cr–5Cr–3Mo, 23Cr–4Ni
25Ni–20Cr–4.5Mo–1.5Cu
10.25
9.66
14.67
14.45
15.99
14.64
15.60
12.25
13.50
10.55
9.70
15.10
14.95
16.12
15.15
15.80
12.50
14.00
10.85
9.74
15.53
15.45
16.25
15.66
16.00
12.75
14.50
11.08
9.94
15.90
15.86
16.41
16.14
16.15
13.00
15.00
11.27
10.13
16.24
16.26
16.57
16.58
16.26
13.25
15.50
11.44
10.31
16.55
16.63
16.72
16.97
16.35
13.50
16.00
11.58
10.49
16.84
16.96
16.85
17.30
16.43
13.75
16.25
11.70
10.65
17.11
17.25
16.98
17.59
16.51
14.00
16.50
11.81
10.81
17.36
17.52
17.10
17.85
16.57
14.25
16.75
11.91
10.96
17.59
17.77
17.22
18.08
16.64
14.50
17.00
12.02
11.11
17.81
18.00
17.34
18.29
16.71
12.13
11.24
18.00
18.23
17.45
18.51
16.78
N08028
31Ni–27Cr–3.5Mo–1.0Cu
14.25
14.50
14.75
15.00
15.25
15.50
15.75
16.00
16.25
16.50
Type or grade
Nominal composition
Carbon and low C, C–Mn, .5Ni–2Mo–V, .75Ni–.2Mo–Cr–V,
.75Ni–.5Mo.3Cr–V, .75Ni–1Mo–.75Cr,
alloy steels
.75Ni–.5Cr–.5Mo–V, 1Ni–.5Cr–.5Mo,
.5Ni–.5Cr–.25Mo–V, .75Ni–.5Cu–Mo
.75Cr–.75Ni–Cu–Al, .75Cr–.5Ni–Cu
C-Mn-Si,.5Cr-.25Mo-Si,1Cr-.Mo-V,
1.25Cr-.5Mo(+ Si), 2Cr-.5Mo, 3Mo-1Mo
Mn–Mo, Mn–Mo–Ni
1.25Ni–1Cr–.5Mo, 1.75Ni–.75Cr–.25Mo,
2Ni–.755Cr–.25Mo, 2Ni–.75Cr–.33Mo,
2.5Ni, 3.5Ni, 3.5 Ni–1.75Cr–.5Mo–V,



500
Stainless steel
(continued)
COPYRIGHT
AS 3857—1999
6
TABLE 4.3 (continued)
Mean coefficient of thermal expansion between 25°C and temperature, K–1 × 10–6 (µm/m.K)
Material
–50
0
50
100
150
200
21.75
22.38
22.54
21.84
21.92
22.25
22.85
23.05
22.35
22.45
22.75
23.32
23.56
22.86
22.98
23.23
23.82
24.06
23.35
23.47
23.72
24.33
24.57
23.85
23.95
24.21
24.83
25.08
24.34
24.44
90Cu–10Zn
80Cu–20Zn
70Cu–30Zn
60Cu–40Zn
16.30
16.63
16.96
17.29
17.62
16.50
16.87
17.25
17.62
17.99
16.70
17.12
17.53
17.95
18.36
16.90
17.36
17.82
18.27
18.73
17.10
17.60
18.10
18.60
19.10
90Cu–10Ni
80Cu–20Ni
70Cu–30Ni
15.50
14.56
14.30
15.74
14.85
14.60
16.00
15.18
114.95
16.26
15.51
15.30
Bronze
16.50
16.74
16.99
Ni, Low C–Ni
Ni–44Fe–18Cr–1Si
Ni–32Cu
Ni–15.5Cr–8Fe
Ni–46Fe–21Cr
Ni–30Fe–21Cr–3Mo–2Cu
Ni–28Mo–5Fe
Ni–16Cr–16Mo
Ni–15.5Cr–16Mo–5.5Fe–4W
11.39
13.95
13.44
11.41
13.14
13.20
10.76
11.00
10.59
11.80
14.35
13.75
11.95
13.80
13.40
10.90
11.10
10.80
8.40
5.85
Type or grade
Nominal composition
Aluminium
alloys
3003 and 3004
5052 and 5454
5083 and 5086
6061
6063
Copper and
copper alloys
Copper
Brasses:
Cu–Ni
Nickel and
nickel alloys
200, 201
330
400 and 405
600
800 and 800H
825
B
C–4
C–276
Design temperature, °C
Titanium and
titanium alloys
1, 2, 3 and 7
Zirconium and
zirconium alloys
702
Zr
705 and 706
Zr–2.5Nb
250
300
350
400
450
17.30
17.84
18.38
18.93
19.47
17.50
18.08
18.67
19.25
19.84
17.70
18.33
18.95
19.58
20.21
17.90
18.57
19.24
19.91
20.57
18.10
18.81
19.52
20.23
20.94
18.30
19.05
19.81
20.56
21.31
18.50
19.29
20.09
20.88
21.68
16.52
15.84
15.65
16.76
16.13
15.95
16.94
16.28
16.10
17.10
16.40
16.20
17.26
16.51
16.30
17.42
16.62
16.40
17.58
16.73
16.50
17.74
16.85
16.60
17.23
17.47
17.71
17.95
18.20
18.44
18.68
18.92
19.16
12.21
14.75
14.06
12.49
14.46
13.60
11.04
11.40
11.01
12.62
15.04
14.36
12.96
14.90
13.80
11.28
11.76
11.35
12.99
15.29
14.65
13.35
15.20
13.98
11.46
11.95
11.67
13.30
15.53
14.92
13.67
15.43
14.15
11.57
12.20
11.98
13.64
15.77
15.16
13.94
15.62
14.31
11.64
12.43
12.28
13.94
15.99
15.37
14.17
15.77
14.48
11.71
12.65
12.55
14.22
16.20
15.56
14.36
15.90
14.63
11.78
12.83
12.79
14.46
16.38
15.73
14.52
16.02
14.78
11.86
12.99
13.00
14.68
16.54
15.88
14.68
16.15
14.92
11.95
13.12
13.20
14.91
16.69
16.02
14.82
16.27
15.05
12.05
13.25
13.40
8.40
8.40
8.46
8.53
8.59
8.66
8.73
8.80
8.86
5.87
5.89
6.30
5.89
5.89
5.89
5.89
5.89
5.89
5.89
COPYRIGHT
500
7
AS 3857—1999
TABLE
4.4
YOUNG MODULUS (MODULUS OF ELASTICITY (E))
Young modulus, GPa
Material
Type or grade
Temperature, °C
Nominal composition
–50
0
50
100
150
200
250
300
350
400
450
500
C ≤ .3%C
C > .3%C
C–.5M0, Mn–.5Mo, Mn–.25Mo, Mn–V
207
206
205
204
203
202
201
200
199
198
197
196
195
194
193
192
191
190
189
187
187
186
184
184
179
178
178
171
170
170
162
161
160
150
149
150
196
193
190
187
184
181
178
175
171
167
163
159
.5Cr–.5Mo, 1Cr–.5Mo,
1.25Cr–.5Mo(+Si), 2Cr–.5Mo
210
207
204
200
196
193
190
187
183
179
174
170
2.25Cr–1Mo, 3Cr–1Mo
5Cr–.5Mo(+Si, +Ti), 7Cr–.5Mo, 9Cr–Mo
217
219
213
215
209
211
206
207
203
204
199
201
196
198
192
194
188
190
184
184
179
176
175
168
Stainless steel
405, 410
429, 430
12Cr–Al, 13Cr,
15Cr, 17Cr
205
202
199
196
192
189
185
181
178
174
166
156
304
316, 317
321
347 and 348
309, 310
18Cr–8Ni
16Cr–12Ni–2Mo, 18Cr–13Ni–3Mo
18Cr–10Ni–Ti
18Cr–10Ni–Nb
23Cr–12Ni, 25Cr–12Ni, 25Cr–20Ni
202
198
194
190
186
183
179
175
172
169
164
161
Carbon and low
alloy steels
.5Ni–.5Mo–V, .5Ni–.5Cr–.25Mo–V
.75Ni–.5Mo–Cr–V, .75Ni–1Mo–.75Cr,
.75Ni–.5Cu–Mo, 1Ni–.4Cr–.5Mo,
.75Cr–.5Ni–Cu, .75Cr–.75Ni–Cu–Al,
2Ni–1Cu, 2.5Ni, 3.5Ni














S31803, 2304
22Cr–5Ni–3Mo, 23Cr–4Ni
205
200
195
190
185
180
175
170
165
160
N08904
25Ni–20Cr–4.5Mo–1.5Cu
200
196
193
190
185
180
175
170
167
165
N08028
31Ni–27Cr–3.5Mo–1.0Cu
204
201
198
195
192
190
185
180
175
170
71
73
74
70
71
72
68
69
70
66
67
68
63
65
65
60
62
62
Aluminium alloys
3003, 3004,6061, 6063
5052, 5054
5083, 5086
(continued)
COPYRIGHT
AS 3857—1999
8
TABLE 4.4 (continued)
Young modulus, GPa
Material
Type or grade
Copper and
copper alloys
Nominal composition
0
50
100
150
200
250
300
350
400
450
500
Bronze
117
105
94
140
152
110
114
103
91
137
148
107
111
100
89
133
144
104
108
97
86
130
140
102
105
95
84
126
137
99
102
92
82
122
133
96
99
89
79
119
129
93
95
86
76
114
124
89
92
83
74
110
120
86
89
80
71
107
116
84
86
77
69
103
112
81
83
75
66
100
108
78
Ni and Low C Ni
Ni–44Fe–18Cr–1Si
Ni–32Cu
Ni–15.5Cr–8Fe
NI–46Fe–21Cr
Ni–30Fe–21Cr–3Mo–2Cu
NI–28Mo–5Fe
Ni–16Cr–16Mo
Ni–15.5Cr–16Mo–5.5Fe–4W
211
197
184
219
200
197
218
209
209
208
194
181
215
197
194
215
206
206
205
191
178
211
194
191
212
203
203
202
188
175
208
191
188
209
200
200
199
185
173
206
189
185
206
197
197
197
183
171
204
187
183
204
195
195
194
181
168
201
185
181
201
193
193
192
179
166
199
183
179
199
191
191
189
177
164
196
180
177
197
188
188
186
174
161
192
177
174
193
185
185
182
170
158
189
174
170
189
181
181
179
167
155
185
170
167
185
177
177
110
108
106
103
100
97
93
88
84
80
101
103
100
102
98
100
95
93
92
86
86
80
80
75
74
71
68
67
Copper > 95%
Brasses:
10 and 20 Zn
30 and 40 Zn
Cu–Ni: 10Ni
20 and 30 Ni
Nickel and
nickel alloys
200, 201
330
400 and 405
600
800 and 800H
825
B
C–4
C276
Titanium and
titanium alloys
1, 2, 3 and 7
Zirconium and
zirconium alloys
702
705 and 706
Temperature, °C
–50
Zr
Zr–2.5Nb
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9
AS 3857 — 1999
5 DESIGN
5.1 Analysis In the method of analysis in this Clause, moments, stresses and
deflections across the tubeplate are calculated. To determine the maximum stresses, full
moment and deflection curves shall be calculated and constructed for several cases for
each design condition (see Clause 5.4).
NOTE: Such calculations are most effectively performed using a computer.
Permissible stresses shall be based on the design strengths specified in the pressure vessel
or boiler Standard applicable to the equipment in which the tubeplate is to be a
component, e.g. AS 1210, AS 1210 Supplement 1 or AS 1228.
To determine metal temperature, a heat transfer analysis shall be undertaken for each
design condition.
NOTE: Guidance in estimating heat transfer coefficients and fouling resistances may be found
in technical publications such as —
(a) for pressure vessels —
(i) Tubular Exchanger Manufacturers Association (TEMA) Standards *;
(ii) Compact Heat Exchangers †; and
(b) for boilers — AS 1228.
5.2
(a)
(b)
(c)
(d)
(e)
(f)
Assumptions The analysis is based on the following assumptions:
The tubeplates are flat, circular and the tube pattern is approximately axisymmetric.
The tube pattern is equilateral triangular (although some approximate results for
square patterns are included).
R > Ri − tp and R > 4.5t p.
Ls > 6ls (if an expansion joint is used, it is placed at least 3ls from the tubeplate).
Channel shell length > 2lc (where channel shell is welded to tubeplate).
tp ≥
(P − d t)
2
Nt ≥ 37.
q > 0.09.
The movement of the tubeplate is not obstructed by anything (e.g. channel baffles),
except the tubes.
(j)
For fixed tubeplates — both have the same flexural rigidity.
(k) Tube bending is ignored.
(l)
Stresses due to temperature gradient across the tubeplate are disregarded except as
specified in Clause 5.8.
For situations falling outside the above, special analysis is required to accurately calculate
stresses.
5.3 Notation and calculation parameters For the purpose of this Standard, notation
and calculation parameters tabulated below apply. The notation for dimensions of
components are shown on Figures 5.3(A), 5.3(B), and 5.3(C).
The symbols for units used in this Clause are combinations of the following:
(a) mm (millimetre).
(b) N (newton).
(c) MPa (megapascal).
(d) °C (degrees Celsius).
(e) K (kelvin).
(f)
rad (radian).
(g)
(h)
(i)
* Standards of Tubular Exchanger Manufacturers Association, Inc.
† Kays, W.M. and London, A.L. Compact Heat Exchangers. 3rd ed. New York: McGraw-Hill, 1984. p. 352.
COPYRIGHT
AS 3857 — 1999
FIGURE 5.3 (in part)
10
NOTATION FOR DIMENSIONS OF HEAT EXCHANGER
COMPONENTS
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11
FIGURE 5.3 (in part)
Quantity
symbol
A, B, C
As
At
a
a1
a2
NOTATION FOR DIMENSIONS OF HEAT EXCHANGER
COMPONENTS
Quantity/Calculation parameter
=
=
=
=
=
=
coefficients of deflection (see Clause 5.5.1)
metal cross-section area of shell
2πRmts
metal cross-sectional area of tubes
πNt(dt − tt)tt
tubeplate characteristic radius
=
=

 0.25
 D  0.25  πR 2 D 
= 
 

K
 2k t 
factor
=
b1 −
=
factor
=
b2 −
2k t b4
ks
2k t b3
ks
AS 3857 — 1999
− (R m − R)e3
− (R m − R)e4
COPYRIGHT
Unit symbol
mm
mm 2
mm 2
mm
AS 3857 — 1999
Quantity
symbol
a3
12
Quantity/Calculation parameter
=
=
a4
=
=
as
=
=
at
=
factor
b3 x R
− e3
a
factor
b4 x R
+ e4
a
fraction of perforated tubeplate exposed to shell side
pressure
 2
d 
1 − Nt  t 
 2R 
fraction of perforated tubeplate exposed to tubeside
pressure
N t(
b1
Unit symbol
=
1 −
=
ber(xR)
dt
− t t) 2
2
R2
NOTE: ber and bei are Lord Kelvin’s modified bessel functions of
the first kind, order zero. An algorithm to generate these functions is
included in Appendix B where calculated values are tabulated.
b2
b3
b4
=
=
=
bei(x R)
ber ′(x R)
xR
bei ′(x R)
xR
∞
ber(x)
=
1 +
i 1
∞
bei(x)
=
i 1
ber ′(x)
=
bei ′(x)
=
D
=
=
 x  4i
( 1)  2 
 
(2i)!2
i
 x  4i 2
( 1)  2 
 
(2i 1)!2
i
d ber(x)
dx
d bei(x)
dx
flexural rigidity to tubeplate
3
p p
E t
2
12(1 − vp )
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N.mm
13
Quantity
symbol
Dc
AS 3857 — 1999
Quantity/Calculation parameter
=
flexural rigidity of channel
Unit symbol
N.mm
3
=
Df
=
E c tc
12(1 − v 2)
flexural rigidity of flange
N.mm
3
=
Ds
=
=
dp
dt
E
=
=
=
Ec
=
Ep
=
Es
=
=
Et
=
e1
=
=
e2
=
=
e3
e4
F
Etf
12 (1 − v 2)
flexural rigidity of shell
N.mm
3
s s
E t
12(1 − v 2)
diameter of holes drilled in tubeplate
outside diameter of tubes
Young modulus of tubeplate as its mean temperature (see
Table 4.4)
Young Modulus of channel at its mean metal temperature
(see Table 4.4)
effective Young modulus of drilled tubeplate
mm
mm
MPa
MPa
MPa
2.89t p/P
E 1 − (1 − q)2 [1 + 1.7q(1 − e
)]
Young modulus of shell at its mean metal temperature (see
Table 4.4)
Young modulus of tube at its mean metal temperature (see
Table 4.4)
factor
MPa
MPa
1/mm
2πDx R
aβ
factor
1/mm
4 (R m − R) k t
β
=
factor
1/mm
=
e1[b2 + (1 − v p)b3] + e2b4
=
factor
=
e1 [b1 − (1 − v p) b4] + e2b3
=
=
=
=
tube span constrain coefficient
1 for unsupported spans between baffles
2 for unsupported spans between a tubeplate and a baffle
4 for unsupported spans between two tubeplates
1/mm
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AS 3857 — 1999
Quantity
symbol
fb
fbt
14
Quantity/Calculation parameter
=
=
design strength of bolts
design strength of elastic (column) buckling of tubes
Unit symbol
MPa
MPa
2
=
Fπ2E t rg
2
(minimum value)
1.5Lu
fj
=
fp
fs
ft
K
=
=
=
=
=
ke
ks
=
=
=
=
kt
=
=
L
Le
Lp
Ls
Lt
Lu
lc
design strength used in calculating joint efficiency (see
Appendix A)
design strength of tubeplate at design temperature
design strength of shell at design temperature
design strength of tubes at design temperature
effective foundation modulus of tubeplate due to support of
tubes
MPa
MPa
MPa
MPa
N/mm3
2k t
πR 2
axial stiffness of expansion joint
axial stiffness of shell
Es As
Ls
N/mm
N/mm
if no expansion joint
1


 1 + L s  with expansion joint
k
E s A s 
 e
total axial stiffness of tubes
N/mm
At Et
Lt
=
=
=
=
distance between outside faces of tubeplates
length removed from shell to accommodate expansion joint
length of expanded portion of tube
effective shell length
=
L − 2t p − L e
=
=
=
=
=
=
free tube length
L for tubes welded to front of tubeplate
L − tp for expanded tubes
L − 2tp for tubes welded to back of tubeplate
unsupported tube span
channel characteristics length
=
 R 2 t 2  0.25
m c



2 
 3(1 − v ) 
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mm
mm
mm
mm
mm
mm
mm
15
Quantity
symbol
ls
Quantity/Calculation parameter
=
Mb
Mc
Me
=
πRg p t (R b − R m)
=
=
‘0’ for clamped plate
circumferential tubeplate moment which produces
circumferential tensile stress on the shell side, per unit
width
tubeplate moment at edge of perforations for a U-tube
bundle, per unit width
=
=
Unit symbol
mm
=
=
=
Mp
shell characteristic length
 R 2 t 2  0.25
m s



2 
 3(1 − v ) 
maximum absolute value of tubeplate moment (see
Clause 5.6)
moment on flange at operating conditions
=
Mmax
AS 3857 — 1999
N.mm
N.mm
2
N.mm/mm
N.mm/mm
(φR − φu)


 1 + 2π R 
β
β 
 u
moment on undrilled portion of tubeplate due to pressure
π(p t − p s)(Ri − R 2)(R m − R)
N.mm
2
=
2
for flanged plate
π(p t − p s)(Rg − R 2)(R g − R)
2
=
Mr
Mu
=
=
=
Np
Nt
P
ps
pt
=
=
=
=
=
for clamped plate
2
radial tubeplate moment with produces radial tensile stress
on the shell side, per unit width
tubeplate moment at centre of simply supported tubeplate,
per unit width
N.mm/mm
N.mm/mm
(p t − p s)(3 + v p)R 2
16
where tube pattern is interrupted by missing tubes due to
shell-side baffle support rods or tube-side baffles etc., Np is
the number of tubes if pattern were complete.
Where the tube pattern is not interrupted as above, Np = Nt
Approximate results may be obtained for square tube
2N t
.
patterns by taking N p =
√3
number of tubes
pitch of tubes in tube pattern
shell-side pressure
tube-side pressure
COPYRIGHT
mm
MPa
MPa
AS 3857 — 1999
Quantity
symbol
q
16
Quantity/Calculation parameter
=
ligament efficiency
=
1 −
dp
Rb
Re
=
=
=
=
Rf
Rg
Ri
Rm
=
=
=
=
P
radius of tubeplate perforation limit
0.525P√Np
pitch circle radius of bolts in flange
largest radius within the convolutions of the expansion
joint to which the shellside pressure is exposed
outside radius of tubeplate flange or rim
outside radius of tubeplate gasket
inside radius of shell
mean shell radius
=
Ri +
R
mm
mm
mm
mm
mm
mm
mm
ts
r
=
rg
=
2
radius from centre of tubeplate to any point on the
tubeplate
radius of gyration of tube
=
0.25√[dt + (d t − 2t t)2]
=
=
=
=
axial stress (see Clause 5.5)
bending stress (see Clause 5.5 and 5.6)
circumferential stress (see Clause 5.5)
fictitious expansion stress
=
E t(αp − αt)(θp − 25)
Sp
Ss
St
tc
tf
tp
ts
tt
W
=
=
=
=
=
=
=
=
=
W1s
=
peak ligament stress (see Clauses 5.5 and 5.6)
stress intensity in shell (see Clause 5.5)
stress intensity in tubes (see Clause 5.5)
channel shell thickness
flange thickness (where no flange is set up)
tubeplate thickness
shell thickness
tube thickness
axial tubeplate deflection at radius r with datum at cold
unpressured conditions
axial movement of shell due to pressure
Sa
Sb
Sc
Se
Unit symbol
mm
mm
2
π(p s − p t )(Ri − R 2)
MPa
MPa
MPa
MPa
MPa
MPa
MPa
mm
mm
mm
mm
mm
mm
mm
2
=
W2s
2k s
+ We
=
axial movement of shell due to Poisson effect
=


Z − (L − 2l ) vR m  p s
s
s

E st s  2

COPYRIGHT
mm
17
Quantity
symbol
W3s
Quantity/Calculation parameter
=
=
W4s
=
=
Ws
W1t
axial thermal growth of shell
AS 3857 — 1999
Unit symbol
mm
(L − t p)αs(θs − 25)
2
axial movement of rim due to rotation
mm
− (M b + M p)(R m − R)
=
β
total axial shell movement
=
W1s + W2s + W3s + W4s
=
axial movement of tube due to pressure
mm
mm
πR (p sa s − p ta t)
2
=
W2t
=
=
W3t
=
=
2k t
axial movement to tube due to Poisson effect
L tv(p s − p t)(d t − t t)
4E tt t
axial thermal growth of tube
=
Wt
=
2
axial initial compression of expansion bellows at
installation
total axial tube movement
=
W1t + W2t + W3t
WR
=
Ws − Wt
x
=
scales radius
xR
=
=
Y
=
=
Z
=
=
αp
=
mm
mm
mm
r
a
dimensionless radius of perforated tubeplate
R
a
stress multiplier
0.06
q
Poisson coefficient
increase in length of unrestrained expansion joint when
1 MPa internal pressure is applied to the convolutions of
the joint
In the absence of better data use —
2.0 +
mm/MPa
π(Re − Ri )
2
=
mm
(L − t p)αt(θt − 25)
We
=
mm
2
2k e
mean coefficient of thermal expansion of tubeplate between
25°C and mean metal temperature (see Table 4.3)
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K -1
AS 3857 — 1999
18
Quantity
symbol
αs
Quantity/Calculation parameter
=
αt
=
βc
=
=
βf
=
=
=
βs
=
=
β
βu
mean coefficient of thermal expansion of shell between
25°C and mean metal temperature (see Table 4.3)
mean coefficient of thermal expansion of tubes between
25°C and mean metal temperature (see Table 4.3)
channel rotation stiffness
0 when channel is bolted or clamped to shell.
flange and rim rotation stiffness
N.mm/rad
(R f + R)
shell rotation stiffness
N.mm/rad

t 
2πR mD s 1 + (1 + p )2
ls 

ls
=
βf + βs + βc
=
edge rotation stiffness of U-tube tubeplate, per unit
circumference
D(1 + v p)
R
3
=
E pt p
12(1 − v p)R
∆
=
α 1α 4 − a 2α 3
ηs
ηt
ηp
=
=
=
weld efficiency of shell
weld efficiency of tubes
joint efficiency of tube-to-tubeplate welds or expanded
joints. (See also Appendix A.)
1.0 for fully radiographed welds
0.85 for spot radiography fo welds
0.75 for automatic but non-radiographed welds
0.5 for manual welds
0.6 for expanded tubes with ≥2 expansion grooves
0.5 for expanded tubes with 1 expansion groove
=
K -1
N.mm/rad
4πD f(R f − R)
0 when tubesheet is bolted or clamped to shell.
total rotation stiffness
=
=
=
=
=
=
K -1

t 
2πR mD c 1 + (1 + p )2
lc 

lc
=
=
=
Unit symbol
0.4L p
dp
(0.4 max) for expanded tubes with no grooves
The above values of ηp apply only under any of the following
conditions:
(a) −ft < Se < 0.
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N.mm/rad
N.mm/mm.rad
19
Quantity
symbol
AS 3857 — 1999
Quantity/Calculation parameter
vp
(b) For welded joints, 0 < Se < 0.5ft.
(c) For expanded joints with grooves, 0 < Se < 0.2ft.
(d) For expanded joints without grooves, 0 < Se < 0.1ft.
If one of these conditions does not prevail, ηp shall be
determined by the method specified in Appendix A.
= mean metal temperature of channel
= mean metal temperature of tubeplate
= mean metal temperature of shell
= mean metal temperature of tubes
= Poisson’s ratio.
In the absence of better data a value of 0.3 may be used.
= effective Poisson’s ratio of drilled tubeplate.
φ
= 0.3 + (1 − q)7.0(0.7 − 10.92q e
= tubeplate rotation
φR
dW
dr
= rim rotation
θc
θp
θs
θt
v
−2.89t p/P
Unit symbol
°C
°C
°C
°C
)
rad
=
=
φu
(M b + M p)
β
U-tube tubeplate edge rotation due to pressure
=
2
rad
(p t − p s)R
rad
2
8βu
Laplacian operator
d2
1 d
+
2
x dx
dx
= Biharmonic operator
= ( 2) 2
=
4
5.4 Design conditions As it is impossible, in general, to predict the most arduous
operating conditions for a heat exchanger, the vessel integrity shall be designed for the
following conditions:
(a)
At nameplate conditions when new.
(b)
At nameplate conditions when corroded (i.e. old).
(c)
Failure of shell side conditions.
(d)
Failure of tubeside conditions.
(e)
Other reasonably expected plant operating conditions, including startup and
shutdown.
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AS 3857 — 1999
5.5
20
Fixed tubeplates
5.5.1 Moments and deflections
determined as follows:
(a)
Using the nomenclature of Clause 5.3 and under the assumptions of Clause 5.2, it
may be shown that —
4
(i)
(ii)
W+W=A
. . . 5.5.1(2)
where A = Wt
. . . 5.5.1(3)
C =
φ =
(e)
5.5.2
(a)
(a1φR − a3W R)
. . . 5.5.1(5)
∆
dW
Bber ′(x) + Cbei ′(x)
=
dr
a
. . . 5.5.1(6)
φ
dφ
+ vp
r
dr
vφ
dφ
+ p
r
dr


(1 − v p)
(1 − v p)

D 

ber′ (x) + C(ber(x) −
bei′ (x))
. . . 5.5.1(8)
=   B( − bei(x) −
2
x
x

a  
For each of the conditions specified in Clause 5.4, W, Mc and Mr should be tabulated
or plotted and the maximum and minimum values found.
In the case of Mc and Mr, the maximum absolute value shall be denoted as M max.
Stresses in tubeplate
Stresses in the tubeplate shall comply with the following:
Maximum mean ligament bending stress is given by —
(i)
(ii)
(b)
. . . 5.5.1(4)
∆


(1 − v p)
(1 − v p)

D 

ber ′(x)) + C (v pber(x) +
bei ′(x)) . . . 5.5.1(7)
=   B ( − v pbei(x) +
2
x
x

a  
The radial moment is given by —
Mr = D
(d)
(a4W R − a2φR)
The circumferential bending moment is given by —
Mc = D
(c)
. . . 5.5.1(1)
whose solution is W = A + Bber(x) + Cbei(x)
B =
(b)
Moments and deflections in a fixed tubeplate may be
Sb =
6Mmax
. . . 5.5.2(1)
2
qtp
Sb shall not exceed 1.5fp
. . . 5.5.2(2)
Peak ligament stress is given by —
(i)
Sp = YSb
. . . 5.5.2(3)
(ii)
Sb shall not exceed 3fp
. . . 5.5.2(4)
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21
(c)
5.5.3
(a)
where the vessel has a cyclic operation, a fatigue analysis shall also be done using
0.5Sp as the stress amplitude.
Stresses in tubes
Stresses in the tubes shall comply with the following:
The circumferential membrane stress is given by —
Sc =
(b)
(i)
Sa =
(ii)
(p t − p s)(d t − t t)
. . . 5.5.3(1)
2t t
The axial membrane stress in the tubes is given by —
2(W − W2t − W3t)E t
. . . 5.5.3(2)
Lt
The absolute maximum of Sa shall not exceed the lesser of —
hp fp and hp ft
(iii)
. . . 5.5.3(3)
The maximum axial compressive stress shall not exceed —
1
. . . 5.5.3(4)
1
 0.5
1


+
2
f 2
f
t
bt


(c)
(i)
The maximum stress intensity Stmax in the tubes is given by the maximum of
the following:
Sc − Samax ,
Sc ,
(ii)
(d)
5.5.4
(a)
Samax ,
Samin
Stresses in shell
. . . 5.5.3(6)
Stresses in the shell shall comply with the following:
Circumferential stress is given by —
ps Rm
. . . 5.5.4(1)
ts
Axial stress is given by —
2[k s W1s − 2k t (Bb4 − Cb3)]
As
. . . 5.5.4(2)
Maximum stress intensity Ssmax is given by the maximum of the following:
Sa − Sc ,
Sc ,
Sa
. . . 5.5.4(3)
The shell stress intensity shall not exceed fsηs
(d)
. . . 5.5.3(5)
Where the vessel has a cyclic operation, a fatigue analysis shall be done using
0.5Stmax as the stress amplitude.
Sa =
(c)
Sc − Samin ,
The tube stress intensity shall not exceed ftηt
Sc =
(b)
AS 3857 — 1999
. . . 5.5.4(4)
Where the vessel has a cyclic operation, a fatigue analysis shall be done using
0.5Ssmax as the stress amplitude.
COPYRIGHT
AS 3857 — 1999
22
5.6 U-tube and bayonet tubeplates
comply with the following:
(a)
Stresses in a U-tube or bayonet tubeplate shall
The radial moment distribution across the tubeplate is given by —



 r  2
Mr = Mu 1 −    + Me

R 
. . . 5.6(1)
The maximum absolute value of Mr, denoted Mmax, will therefore be either
Mu + Me at the centre, or
Me
(b)
at the edge
. . . 5.6(2)
Mean ligament bending stress is given by —
Sb =
6Mmax
. . . 5.6(3)
2
qtp
Sb shall not exceed 1.5fp
(c)
(d)
. . . 5.6(4)
Peak ligament stress is given by —
Sp = YSb
. . . 5.6(5)
Sp should not exceed 3fp
. . . 5.6(6)
Where the vessel has a cyclic operation, a fatigue analysis shall be done using 0.5Sp
variation as the stress amplitude.
5.7 Floating tubeplates Floating tubeplates may be analysed using the method in
Clause 5.5 by taking ks as a very small value e.g. 10 N/mm.
5.8 Temperature gradients through the tubeplates Where thermal stresses through
the tubeplate are expected to be severe, particularly under cyclic conditions, suitable
allowances shall be made in the design calculations, or provision made to reduce the
severity of the thermal stresses.
NOTE: The temperature gradients that arise in the great majority of heat exchangers, have little
effect on maximum tubeplate stresses and therefore can often be safely neglected.
COPYRIGHT
23
APPENDIX
AS 3857 — 1999
A
TUBE-TO-TUBEPLATE JOINT — DETERMINATION OF AXIAL
BREAKING LOAD AND JOINT EFFICIENCY
(Normative)
A1 SCOPE This Appendix specifies a method of determining the axial force required
to cause mechanical failure of the tube or joint of a tube-to-tubeplate joint and of
calculating its joint efficiency.
A2 APPLICATION The method shall be used where conditions (a) to (d) in the
notation for ηp in Clause 5.3 do not prevail or where it is desired to use a higher joint
efficiency than that specified in the notation for ηp, as appropriate.
A3 APPARATUS The apparatus for the test comprises 12 test blocks complying with
Clause A4 and a means of applying an axial force to the central tube in each test block
and measuring the force to an accuracy of 1 percent of the breaking force.
A4 TEST BLOCK Each test block shall comprise a central tube and one row of tubes
surrounding it, all mounted in the test block i.e. 7 tubes for a triangular tube layout and
9 tubes for a square tube layout, as indicated in Figure A1.
The dimension of the tubes and the tube pitch in the test block shall be the same as in the
tubeplate it represents, except that the test block may be thinner but not thicker than the
tubeplate. Provision shall be made to apply axial loading to the central tube only.
The methods, materials and procedures used to join the tubes to the test block shall be
identical to those used in the tubeplate it represents. The central tube shall not be the first
or the last tube joined to the test block.
A5
PROCEDURE
(a)
Before the tests are carried out, heat all the test blocks to a temperature 10°C above
the maximum design temperature, hold at that temperature for 6 h and then allow to
cool slowly (50°C/h maximum rate).
(b)
Test six test blocks at ambient temperature by applying axial loading to the central
tube of each test block in turn until the tube or joint breaks. Record the breaking
force for each ambient temperature test.
(c)
Heat the remaining six test blocks to the maximum design temperature and test at
that temperature by applying axial loading to the central tube of each test block in
turn until the tube or joint breaks. Record the breaking force for each test at
maximum design temperature.
A6
CALCULATIONS
(a)
(i)
Calculate the mean axial breaking force (G) of the batch of six test blocks
tested at ambient temperature.
(ii)
Using the mean axial breaking force from Item (i) above, calculate the joint
efficiency from the following equation:
ηp =
The test procedure shall be as follows:
The joint efficiency (ηp) shall be calculated as follows:
G
2π(d t − t t)t t f j
. . . A(1)
where fj = lesser value of fp and ft at ambient temperature.
COPYRIGHT
AS 3857 — 1999
(b)
24
Repeat procedures in Item (a) above for the batch of six test blocks tested at
maximum design temperature, but in Equation A(1) use —
fj = lesser value of fp and ft at maximum design temperature.
(c)
The joint efficiency (ηp) shall be taken as the lesser of the values determined by
Items (a) and (b) above but shall not exceed 1.0.
FIGURE A1
TEST APPARATUS TO MEASURE TUBE AXIAL FAILURE LOAD
COPYRIGHT
25
APPENDIX
AS 3857 — 1999
B
LORD KELVIN’S MODIFIED BESSEL FUNCTIONS
(Normative)
Figure B1 provides an algorithm for generating Lord Kelvin’s modified Bessel functions.
Table B1 lists values for Lord Kelvin’s modified Bessel functions of the first kind, order
zero.
COPYRIGHT
AS 3857 — 1999
26
FIGURE B1
ALGORITHM FOR GENERATING LORD KELVIN’S MODIFIED
BESSEL FUNCTIONS
COPYRIGHT
27
TABLE
AS 3857 — 1999
B1
LORD KELVIN’S MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND,
ORDER ZERO
x
0.00
0.10
0.20
0.30
0.40
ber
1.00000
1.00000
0.99998
0.99987
0.99960
bei
0.00000
0.00250
0.01000
0.02250
0.04000
ber′
0.00000
−0.00006
−0.00050
−0.00169
−0.00400
bei′
0.00000
0.05000
0.10000
0.14999
0.19997
0.50
0.60
0.70
0.80
0.90
0.99902
0.99798
0.99625
0.99360
0.98975
0.06249
0.08998
0.12245
0.15989
0.20227
−0.00781
−0.01350
−0.02143
−0.03199
−0.04554
0.24992
0.29980
0.34956
0.39915
0.44846
1.00
1.10
1.20
1.30
1.40
0.98438
0.97714
0.96763
0.95543
0.94008
0.24957
0.30173
0.35870
0.42041
0.48673
−0.06245
−0.08308
−0.10781
−0.13697
−0.17093
0.49740
0.54581
0.59352
0.64034
0.68601
1.50
1.60
1.70
1.80
1.90
0.92107
0.89789
0.86997
0.83672
0.79752
0.55756
0.63273
0.71204
0.79526
0.88212
−0.21001
−0.25454
−0.30484
−0.36118
−0.42384
0.73025
0.77274
0.81310
0.85093
0.88574
2.00
2.10
2.20
2.30
2.40
0.75173
0.69869
0.63769
0.56805
0.48905
0.97229
1.06539
1.16097
1.25853
1.35749
−0.49307
−0.56906
−0.65200
−0.74202
−0.83920
0.91701
0.94418
0.96661
0.98361
0.99443
2.50
2.60
2.70
2.80
2.90
0.39997
0.30009
0.18871
0.06511
−0.07137
1.45718
1.55688
1.65574
1.75285
1.84718
−0.94358
−1.05513
−1.17375
−1.29926
−1.43141
0.99827
0.99426
0.98149
0.95897
0.92566
3.00
3.10
3.20
3.30
3.40
−0.22138
−0.38553
−0.56438
−0.75841
−0.96804
1.93759
2.02284
2.10157
2.17231
2.23345
−1.56985
−1.71410
−1.86362
−2.01769
−2.17550
0.88048
0.82230
0.74992
0.66214
0.55769
3.50
3.60
3.70
3.80
3.90
−1.19360
−1.43531
−1.69326
−1.96742
−2.25760
2.28325
2.31986
2.34130
2.34543
2.33002
−2.33606
−2.49825
−2.66078
−2.82216
−2.98074
0.43530
0.29366
0.13149
−0.05253
−0.25965
4.00
4.10
4.20
4.30
4.40
−2.56342
−2.88431
−3.21948
−3.56791
−3.92831
2.29269
2.23094
2.14217
2.02365
1.87256
−3.13465
−3.28182
−3.41995
−3.54652
−3.65877
−0.49114
−0.74817
−1.03186
−1.34325
−1.68325
4.50
4.60
4.70
4.80
4.90
−4.29909
−4.67836
−5.06388
−5.45308
−5.84294
1.68602
1.46104
1.19460
0.88366
0.52515
−3.75368
−3.82801
−3.87824
−3.90060
−3.89106
−2.05263
−2.45201
−2.88180
−3.34218
−3.83308
5.00
5.10
5.20
5.30
5.40
−6.23008
−6.61065
−6.98035
−7.33436
−7.66739
0.11603
−0.34666
−0.86584
−1.44426
−2.08452
−3.84534
−3.75890
−3.62697
−3.44453
−3.20636
−4.35414
−4.90464
−5.48350
−6.08923
−6.71986
5.50
5.60
5.70
5.80
5.90
−7.97360
−8.24658
−8.47937
−8.66445
−8.79367
−2.78898
−3.55975
−4.39858
−5.30685
−6.28545
−2.90703
−2.54096
−2.10240
−1.58551
−0.98438
COPYRIGHT
−7.37291
−8.04536
−8.73357
−9.43325
−10.13939
(continued)
AS 3857—1999
28
TABLE
B1 (continued)
x
6.00
6.10
6.20
6.30
6.40
ber
−8.85832
−8.84908
−8.75606
−8.56879
−8.27625
bei
−7.33475
−8.45449
−9.64374
−10.90074
−12.22286
ber′
−0.29308
0.49429
1.38352
2.38035
3.48985
bei′
−10.84622
−11.54718
−12.23481
−12.90078
−13.53576
6.50
6.60
6.70
6.80
6.90
−7.86689
−7.32869
−6.64918
−5.81551
−4.81456
−13.60651
−15.04699
−16.53842
−18.07363
−19.64399
4.71738
6.06746
7.54418
9.15098
10.89051
−14.12942
−14.67041
−15.14626
−15.54341
−15.84711
7.00
7.10
7.20
7.30
7.40
−3.63293
−2.25715
−0.67370
1.13080
3.16946
−21.23940
−22.84808
−24.45648
−26.04919
−27.60877
12.76452
14.77372
16.91758
19.19421
21.60012
−16.04149
−16.10948
−16.03286
−15.79221
−15.36700
7.50
7.60
7.70
7.80
7.90
5.45496
7.99938
10.81396
13.90892
17.29313
−29.11571
−30.54826
−31.88236
−33.09154
−34.14683
24.13012
26.77706
29.53136
32.38218
35.31443
−14.73560
−13.87533
−12.76255
−11.37273
−9.68062
8.00
8.10
8.20
8.30
8.40
20.97396
24.95690
29.24521
33.83976
38.73840
−35.01673
−35.66708
−36.06112
−36.15940
−35.91983
38.31133
41.35277
44.41531
47.47210
50.49241
−7.66032
−5.28548
−2.52956
0.63410
4.23183
8.50
8.60
8.70
8.80
8.90
43.93587
49.42311
55.18692
61.20974
67.46872
−35.29770
−34.24576
−32.71432
−30.65138
−28.00288
53.44162
56.28083
58.96671
61.45136
63.68195
8.28952
12.83214
17.88338
23.46546
29.59828
9.00
9.10
9.20
9.30
9.40
73.93573
80.57644
87.34994
94.20846
101.09633
−24.71278
−20.72355
−15.97642
−10.41165
−3.96931
65.60077
67.14489
68.24618
68.83119
68.82112
36.29938
43.58300
51.45962
59.93556
69.01181
9.50
9.60
9.70
9.80
9.90
107.95003
114.69714
121.25605
127.53566
133.43444
3.41057
11.78702
21.21751
31.75755
43.45911
68.13184
66.67398
64.35308
61.06958
56.71986
78.68389
88.94047
99.76283
111.12426
122.98843
10.00
10.10
10.20
10.30
10.40
138.84047
143.6306
147.6705
150.8141
152.9034
56.37046
70.5344
85.9873
102.7584
120.8673
51.19526
44.3839
36.1707
26.4376
15.0657
135.30930
148.0293
161.0788
174.3751
187.8208
10.50
10.60
10.70
10.80
10.90
153.7686
153.2277
151.0869
147.1407
141.1724
140.3238
161.1251
183.2546
206.6809
213.3539
1.9344
−13.0758
−30.0828
−49.2021
−70.5436
201.3036
214.6944
227.8464
240.5946
252.7541
11.00
11.10
11.20
11.30
11.40
132.9544
122.2492
108.8104
92.3834
72.7074
257.2052
284.1440
312.0555
340.7999
370.2077
−94.2119
−120.3022
−148.8993
−180.0760
−213.8880
264.1194
274.4635
283.5370
291.0677
296.7594
11.50
11.60
11.70
11.80
11.90
49.5166
22.5436
−8.4831
−43.8279
−83.7528
400.0798
430.1830
460.2438
489.9698
518.9997
−250.3744
−289.5517
−331.4116
−375.9191
−423.0057
300.2921
301.3214
299.4785
294.3705
285.5809
(continued)
COPYRIGHT
29
TABLE
AS 3857—1999
B1 (continued)
x
12.00
12.10
12.20
12.30
12.40
ber
−128.5116
−178.3448
−233.4760
−294.1096
−360.4213
bei
546.9486
573.3812
597.8151
619.7196
638.5122
ber′
−472.5688
−524.4648
−578.5058
−634.4568
−692.0275
bei′
272.6700
255.1767
232.6197
204.4986
170.2984
12.50
12.60
12.70
12.80
12.90
−432.5575
−510.6250
−594.6858
−684.7530
−780.7775
653.5589
664.1720
669.6094
669.0752
661.7186
−750.8715
−810.5780
−870.6682
−930.5921
−989.7195
129.4895
81.5341
25.8888
−37.9919
−110.6466
13.00
13.10
13.20
13.30
13.40
−882.6466
−990.1694
−1103.0704
−1220.9831
−1343.4330
646.6357
622.8701
589.4164
545.2207
489.1880
−1047.3396
−1102.6526
−1154.7662
−1202.6934
−1245.3447
−192.6057
−284.3801
−386.4545
−499.2827
−623.2706
13.50
13.60
13.70
13.80
13.90
−1469.8363
−1599.4809
−1731.5192
−1864.9611
−1998.6539
420.1827
337.0389
238.5661
123.5542
−9.2095
−1281.5285
−1309.9447
−1329.1844
−1337.7285
−1333.9457
−758.7745
−906.0818
−1065.4014
−1236.8551
−1420.4528
14.00
14.10
14.20
14.30
14.40
−2131.2812
−2261.3431
−2387.1494
−2506.8125
−2618.2290
−160.9377
−332.8218
−526.0203
−741.6483
−980.7462
−1316.0930
−1282.3215
−1230.6708
−1159.0808
−1065.3966
−1616.0894
−1823.5167
−2042.3303
−2271.9580
−2511.6257
14.50
14.60
14.70
14.80
14.90
−2719.0803
−2806.8156
−2878.6496
−2931.5571
−2962.2652
−1244.2754
−1533.0807
−1847.8715
−2189.2048
−2557.4389
−947.3726
−802.6876
−628.9560
−423.7367
−184.5624
−2760.3541
−3016.9222
−3279.8521
−3547.3942
−3817.4872
15.00
15.10
15.20
15.30
15.40
−2967.2545
−2942.7568
−2884.7591
−2789.0061
−2651.0138
−2952.7079
−3374.9042
−3823.6121
−4298.1033
−4797.2623
91.0553
405.5874
761.4658
1161.0648
1606.6424
−4087.7552
−4355.4670
−4617.5208
−4870.4297
−5110.2827
15.50
15.60
15.70
15.80
15.90
−2466.0737
−2229.2771
−1935.5341
−1579.5882
−1156.0681
−5319.5798
−5863.0758
−6425.2666
−7003.1339
−7593.0377
2100.3324
2644.0741
3239.5761
3888.2846
4591.2872
−5332.7431
−5533.0137
−5705.8270
−5845.4348
−5945.5849
16.00
16.10
16.20
16.30
16.40
−659.4969
−84.3614
574.8540
1323.5915
2167.2146
−8190.7100
−8791.1649
−9388.6698
−9976.6777
−10547.8219
5349.3019
6162.5669
7030.7970
7953.0847
8927.8925
−5999.5236
−5999.9828
−5939.1841
−5808.8462
−5600.1845
16.50
16.60
16.70
16.80
16.90
3110.8499
4159.3616
5317.2477
6588.5154
7976.6708
−11903.8000
−11605.3721
−12072.3061
−12483.3305
−12826.1300
9952.8636
11024.8032
12139.5694
13291.9547
14475.6755
−5303.9433
−4910.4126
−4409.4638
−3790.6044
−3042.9824
17.00
17.10
17.20
17.30
17.40
9484.4544
11113.8061
12865.7016
14739.9655
16735.2544
−13087.2682
−13252.1987
−13305.2421
−13229.5850
−13007.2774
15683.1382
16905.4220
18132.1517
19351.3684
20549.5171
−2155.5202
−1116.9456
84.1083
1458.9723
3018.9318
17.50
17.60
17.70
17.80
17.90
18848.6712
21075.7234
23410.0964
25843.4051
28365.1714
−12619.2610
−12045.3991
−11264.5262
−10254.5367
−8992.3907
21711.2023
22819.1805
23854.2404
24795.0954
25618.3709
4774.9354
6737.5457
8916.7459
11321.7045
13960.7555
(continued)
COPYRIGHT
AS 3857—1999
30
TABLE
B1 (continued)
x
18.00
18.10
18.20
18.30
18.40
ber
30962.3273
33619.1747
36317.1098
39034.3380
41745.8455
bei
−7454.3370
−5615.9739
−3452.4240
−938.5724
1950.9153
ber′
26298.4235
26807.3544
27114.9443
27188.6261
26993.4767
bei′
16840.8964
19967.7186
23345.0938
26974.8103
30856.5409
18.50
18.60
18.70
18.80
18.90
44422.8529
47032.7899
49539.0163
51900.5603
54072.0898
5241.0567
8956.4532
13120.9250
17757.0579
22886.1655
26492.2221
25645.2886
24410.8689
22745.0619
20601.8778
34987.0917
39360.3156
43966.6669
48792.7063
53821.0543
19.00
19.10
19.20
19.30
19.40
56003.4505
57639.6801
58920.8170
59781.7741
60152.3181
28527.3154
34697.1857
41409.4461
48674.0326
56497.0824
17933.6095
14690.9414
10823.2541
6279.0486
1005.9763
59029.4005
64390.4142
69871.1856
75432.6411
81029.4817
19.50
19.60
19.70
19.80
19.90
59956.9331
59114.9081
57540.3843
55142.5405
51825.5972
64879.4235
73816.3902
83296.9126
93302.4965
103807.1250
−5048.1895
−11935.3650
−19706.4832
−28410.6475
−38095.0617
86609.0543
92111.2849
97468.0882
102602.7992
107430.1049
20.00
47489.3703
114775.1974
−48803.1979
111855.0252
COPYRIGHT
31
APPENDIX
AS 3857 — 1999
C
SAMPLE CALCULATION SHEETS AND WORKED EXAMPLES
(Informative)
C1 SCOPE This Appendix sets out sample calculation sheets for fixed tubeplates and
for the tubeplate of a U-tube heat exchanger. It also provides worked examples for such
types of tubeplates.
COPYRIGHT
AS 3857—1999
32
CALCULATED RESULTS
C2 SAMPLE CALCULATIONS
C2.1 Fixed tubeplate calculation
Length
Radius
Area fraction
Metal X-area
Axial stiffness
Flex. constants
VESSEL IDENTIFICATION:
VESSEL CONDITION:
SKETCH:
Unit
rg
at
At
kt
fbt
=
=
=
=
=
=
Dc
lc
=
=
βf
=
Pressure moments
βc
Df
Ls
Rm
as
As
ks
=
=
=
=
Ds
ls
=
=
βs
Mb
=
=
R
q
mm
mm
=
=
Ep
νp
D
a
XR
β
Mp
=
=
=
=
=
=
=
W4s
=
mm2
N/mm
MPa
N.mm
mm
N.mm/rad
N.mm
MISCELLANEOUS CONSTANTS
Tubes
Shell
Tubeplate
Unit
INPUT DATA
Thickness
tt
Number
Dimensions—
Nt =
Bafl.-Bafl.:
Bafl.-T’sht:
T’sht-T’sht:
Expn joint—
stiffness
Poisson coeff.
Length
=
ts
tc
=
= (0 if none)
Ri =
Rg =
dt
Lt
Lu
Lu
Lu
=
=
= (F = 1)
= (F = 2)
= (F = 4)
L
=
tp
tf
Np
Rb
Rf
dp
P
=
=
=
=
=
=
=
mm
mm
We =
N/mm
mm/MPa
mm
θp =
MPa
°C
pt
θt
=
=
ps
θs
=
=
ft
Et
=
=
Mean exp coeff
Joint efficiency
αt =
ηt =
fs
Es
Ec
αs
ηs
=
=
=
=
=
fp
E
=
=
αp =
ηp =
W2t
W2s
Ws
=
=
=
W3t
W3s
WR
=
=
=
b1
e1
a1
∆
=
=
=
=
b2
e2
a2
=
=
=
b3
e3
a3
=
=
=
φR
b4
e4
a4
=
=
=
=
A
=
B
=
C
=
Displacement W
W − W2t − W3t
Radial moment Mr
Circumferential moment Mc
Minimum
Tubeplate:
Mean ligament bending Sb
Ligament peak Sp
Tubes:
Circumferential Sc
Axial—Maximum & min. Sa
Axial comp.—Maximum Sa
Stress intensity St max.
Shell:
Circumferential and axial Sc, S a
Stress intensity Ss max.
COPYRIGHT
1/mm
mm
Max. abs.
mm
mm
N.mm/mm
N.mm/mm
=
Stresses
MPa
MPa
MPa
1/K
mm
mm
mm
rad
Stress multiplier Y =
Maximum
OPERATING CONDITIONS
Pressure
Mean metal temp.
Material
Design strength
Young modulus
=
=
=
STRESS CALCULATIONS
mm
mm
mm
mm
mm
mm
mm
ke = (0 if none)
Z = (0 if none)
Le =
W1t
W1s
Wt
Limit
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
33
AS 3857—1999
C2.2 U-tube/tubeplate calculation
VESSEL IDENTIFICATION:
VESSEL CONDITION:
SKETCH:
Tubeside
Shellside
Tubeplate
Unit
INPUT DATA
Thickness
tc
=
Number
Dimensions
Nt
=
dt
ts
=
Ri
Rg
=
=
=
tp
tf
Np
Rb
Rf
dp
P
=
=
=
=
=
=
=
mm
mm
mm
mm
mm
mm
OPERATING CONDITIONS
Pressure
Mean metal temp.
Material
Design strength
Young modulus
pt
θc
=
=
ps
θs
=
=
θp
=
MPa
°C
Ec
=
Es
=
fp
E
=
=
MPa
MPa
R
q
Ep
D
=
=
=
=
mm
CALCULATED RESULTS
Rm =
νp =
Df =
βf
=
Dc =
lc =
βc =
Me
STRESS CALCULATION
Ds
ls
βs
Mb
φR
=
=
=
=
=
Mu =
β
Mp
φu
βu
Mmax
=
=
=
=
=
MPa
N.mm
mm
N.mm/rad
N.mm
rad
N/rad
N.mm/mm
Stress multiplier Y =
Maximum
Limit
Unit
MPa
MPa
Mean Ligament Sb
Ligament peak Sp
COPYRIGHT
AS 3857—1999
34
C3 WORKED EXAMPLES
C3.1 Fixed tubeplate calculation
VESSEL IDENTIFICATION:
VESSEL CONDITION:
SKETCH:
CALCULATED RESULTS*
Unit
Length
Test case to AS 1210 Supplement 1
Class 1H
New—uncorroded
mm
Ls
=
2380.0
Rm
=
415.00
R
=
379.40
0.439 74
q
=
0.2031
Radius
rg
=
8.303
Area fraction
at
=
0.602 31
as
=
Metal X-area
At
=
73 513
As
=
26 075
mm 2
Axial stiffness
kt
=
5 822 251
ks
=
2 136 415
N/mm
Flex. constants
f bt
=
534.329
Df
βf
=
=
3.857E + 09
6.647E + 09
Dc
=
0.000E + 00
lc
=
0.000
βc
=
0.000E + 00
Pressure moments
Ep
=
28 604
νp
=
0.441
mm
MPa
Ds
=
1.786E + 07
D
=
6.391E + 08
N.mm
ls
=
50.117
a
=
70.581
mm
XR
=
5.375
β
=
1.206E + 10
N.mm/rad
Mp
=
2 026 499
N.mm
W4s
=
−0.203
φR
=
5.71E−0.3
rad
1/mm
Bs
=
5.414E + 09
Mb
=
6.69E + 07
MISCELLANEOUS CONSTANTS
Tubes
Shell
Tubeplate
Unit
Wlt
=
−0.038
W2t
=
−0.017
W3t
=
1.107
Wls
=
−0.027
W2s
=
−0.036
W3s
=
1.891
Wt
=
1.052
Ws
=
1.625
WR
=
0.572
b1
=
−7.588
b2
e1
a1
=
0.025
e2
=
−19.270
a2
∆
=
5.106
A
b3
=
−0.608
b4
=
−1.221
=
0.069
e3
=
−0.141
e4
=
−0.217
=
9.117
a3
=
0.095
a4
=
−0.310
=
1.052
B
=
−0.045
C
=
−0.032
STRESS CALCULATIONS
Number
Dimensions—
Bafl.-Bafl.:
Bafl.-T’sht:
T’sht-T’sht:
Exp’n joint—
Stiffness
Poisson coeff.
Length
Nt
dt
Lt
Lu
Lu
Lu
=
=
=
=
=
=
=
2.0
ts
tc
=
=
10.0
0
Ri
Rg
=
=
410
440
L
=
2 500
500
25.4
2 500
410 (F = 1)
500 (F = 2)
0 (F = 4)
ke
Z
Le
=
=
=
0
0
0
tp
tf
Np
Rb
Rf
dp
P
=
=
=
=
=
=
=
We =
60.0
60.0
510
470
500
25.5
32.0
0.0
mm
mm
mm
mm
mm
mm
mm
mm
mm
pt
θt
AS
ft
Et
Mean exp coeff.
Joint efficiency
αt
ηt
Minimum
1.455
0.365
23 830
16 397
0.986
−0.104
−2976
−2976
Stresses
Tubeplate:
Mean ligament bending S b
Ligament peak Sp
195.5
448.8
Max. abs.
Unit
23 830
mm
mm
N.mm/mm
N.mm/mm
Limit
Unit
0.365
268.5
537.0
MPa
MPa
84.5
161.1
143.7
MPa
MPa
MPa
MPa
148.0
MPa
MPa
Tubes:
N/mm
mm/MPa
mm
OPERATING CONDITIONS
Pressure
Mean metal temp.
Material
Design strength
Young modulus
Displacement W
W − W2t − W3t =
Radial moment Mr
Circumferential moment Mc
mm
Stress multiplier Y = 2.295
Maximum
tt
mm
mm
−1.921
INPUT DATA
Thickness
mm
Circumferential Sc
Axial—Maximum & min. Sa
Axial comp.—Maximum Sa
Stress intensity St max.
8.8
57.7
16.5
57.7
Circumferential and axial Sc, S a
Stress intensity Ss max.
20.8
56.6
−16.5
Shell:
=
2.0
=
100.0
1836 TW9
=
169.0
=
198 000
=
=
0.000 012 1
0.85
ps
θs
AS
fs
Es
Ec
αs
ηs
=
0.5
=
150.0
1548-7-430
=
148.0
=
195 000
=
195 000
=
0.000 012 4
=
1.0
θp
AS
fp
E
ηp
=
150
1548-5-490
=
179.0
=
195 000
=
MPa
°C
MPa
MPa
MPa
1/K
−35.9
* In this worked example, some mathematical symbols are expressed in computer style, e.g. ‘E + 09’ is used for ‘× 109’, ‘E − 03’ is used
for ‘× 10-3’
0.5
COPYRIGHT
35
FIGURE C1
FIXED TUBEPLATE ANALYSIS
COPYRIGHT
AS 3857—1999
AS 3857—1999
36
C3.2 U-tube/tubeplate calculation
VESSEL IDENTIFICATION:
VESSEL CONDITION:
SKETCH:
Test case
New—uncorroded
Tubeside
Shellside
Tubeplate
Unit
INPUT DATA
Thickness
tc
=
0
Number
Dimensions
Nt
=
280
dt
=
ts
=
0
Ri
Rg
=
=
300
370
25.4
tp
tf
Np
Rb
Rf
dp
P
=
=
mm
mm
60.0
60.0
285
410
370
25.5
32.0
=
=
=
=
=
mm
mm
mm
mm
OPERATING CONDITIONS
Pressure
Mean metal temp.
Material
Design strength
Young modulus
pt
=
1.75
θc =
100.0
AS 1548-7-430
Ec
=
198 000
ps
=
θs =
AS 1548-7-430
0.5
200
Es
=
192000
Rm
νp
=
=
300.00
0.441
150.0
MPa
°C
108.0
195 000
MPa
MPa
=
=
=
=
283.62
0.2031
28 604
6.391E + 08
mm
=
=
=
=
=
6.406E + 09
9.58E + 06
3.87E − 03
3.247E + 06
17569
θp
=
AS 1548-7-430
=
fp
E
=
CALCULATED RESULTS
Df
=
3.87E + 09
βf
=
6.406E + 09
STRESS CALCULATION
Mean Ligament Sb
Ligament peak Sp
Dc
lc
βc
=
=
=
0.000E + 00
0.000
0.000E + 00
Ds
ls
βs
Mb
φR
=
=
=
=
=
0.000E + 00
0.000
0.000E + 00
0.000E + 00
1.49E − 03
Me
=
−13 126
Mu
=
21 623
R
q
Ep
D
β
Mp
φu
βu
Mmax
MPa
N.mm
mm
N.mm/rad
N.mm
rad
N/rad
N.mm/mm
Stress multiplier Y = 2.295
Maximum
Limit
144.2
330.9
162.0
324.0
COPYRIGHT
Unit
MPa
MPa