ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules

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2010 SECTION VIII, DIVISION 2

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(a) Equilateral Triangular Pattern

(b) Square Pattern

Note:

(Perimeter) is the length of the heavy line

Figure 4.18.14 – Tube Layout Perimeter

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(b) Hemispherical Channel

NOTE: Head Shall Be 180 Degrees With

No Intervening Cylinders

(a) Cylindrical Channel

NOTE: Length of Cylinder Shall Be >

1.8 D

Figure 4.18.15 - Integral Channels

Figure 4.18.16 - Some Representative Configurations Describing the Minimum Required Thickness of

the Tubesheet Flanged Extension,

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4.19 Design Rules for Bellows Expansion Joints

4.19.1 Scope

The rules in paragraph 4.19 apply to single or multiple layer bellows expansion joints, unreinforced, reinforced

or toroidal, as shown in Figure 4.19.1, subject to internal or external pressure and cyclic displacement. The

bellows shall consist of single or multiple identically formed convolutions. They may be as formed (not heat-

treated), or annealed (heat-treated). The suitability of an expansion joint for the specified design pressure,

temperature, and axial displacement shall be determined by the methods described herein.

4.19.2 Conditions of Applicability

The design rules of this paragraph are applicable only when the following conditions of applicability are

satisfied:

a) The bellows length shall be such that:

Nq D

≤

b) The bellows nominal thickness shall be such that:

5(0.2.)nt mm in

≤

c) The number of plies shall be such that:

≤

d) The displacement shall be essentially axial. However angular and/or lateral deflection inherent in the fit-

up of the expansion joint to the pressure vessel is permissible provided the amount is specified and is

included in the expansion joint design (see paragraph 4.19.3.1.d).

e) These rules are valid for design temperatures up to 425°C (800°F).

f) The fatigue equations given in Table 4.19.5, Table 4.19.7 and Table 4.19.10 are valid for austenitic

chromium-nickel steels, UNS N066XX and UNS N04400. For other materials, the fatigue evaluation

shall meet the requirements of paragraph 4.19.3.2.b.

4.19.3 Design Considerations

4.19.3.1 General

a) Expansion joints used as an integral part of heat exchangers or other pressure vessels shall be

designed to provide flexibility for thermal expansion and also to function as a pressure containing

element.

b) The vessel Manufacturer shall specify the design conditions and requirements for the detailed design

and manufacture of the expansion joint. Use of the specification sheet shown in paragraph 4.19.17 is

recommended.

c) In all vessels with integral expansion joints, the hydrostatic end force caused by pressure and/or the joint

spring force shall be resisted by adequate restraint elements (e.g., exchanger tubes or shell, external

restraints, anchors, etc.). The primary stress in these restraining elements shall satisfy paragraph

4.1.6.1.

d) The expansion joints shall be provided with bars or other suitable members for maintaining the proper

overall length dimension during shipment and vessel fabrication. Expansion bellows shall not be

extended, compressed, rotated, or laterally offset to accommodate connecting parts, which are not

properly aligned, unless the design considers such movements (see paragraph 4.19.8).

e) The minimum thickness limitations of paragraph 4.1 do not apply to bellows designed to this paragraph.

f) This paragraph does not contain rules to cover all details of design and construction. The criteria in this

paragraph are, therefore, established to cover common expansion joint types, but it is not intended to

limit configurations or details to those illustrated or otherwise described herein. However, when

evaluating designs which differ from the basic concepts of this paragraph (e.g., asymmetric geometries

or loadings, external pressure, materials, etc.), the design shall comply with the requirements of Part 5.

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g) Longitudinal weld seams that comply with paragraphs 4.19.9 and 4.19.10 shall be considered to have a

joint efficiency of 1.0.

h) The elastic moduli, yield strength, and allowable stresses shall be taken at the design temperatures.

However, when performing the fatigue evaluation in accordance with 4.19.5.7 (unreinforced bellows),

4.19.6.7 (reinforced bellows) and 4.19.7.7 (toroidal bellows), it is permitted to use the operating metal

temperature instead of design temperature.

4.19.3.2 Fatigue

a) Cumulative Damage – If there are two or more types of stress cycles, which produce significant

stresses, their cumulative effect shall be evaluated as given below.

1) Designate the specified number of times each type of stress cycle of types 1, 2, 3, etc., will be

repeated during the life of the expansion joint as

123

, , nnn, etc., respectively. When determining

123

, , nnn, etc., consideration shall be given to the superposition of cycles of various origins, which

produce a total stress difference range greater than the stress difference ranges of the individual

cycles. For example, if one type of stress cycle produces 1000 cycles of a stress difference

variation from zero to +60,000 psi and another type of stress cycle produces 10,000 cycles of a

stress difference variation from zero to -50,000 psi, the two types of cycles to be considered are

defined by the following parameters:

i) Type 1 cycle:

1000; 60000 50000 110,000

nS psi==+−=

ii) Type 2 cycle:

10000 1000 9000; 0 50000 50,000

nS psi=−= =+−=

2) For each value

S ,

S , etc., use the applicable design fatigue curve to determine the

maximum number of repetitions which would be allowable if this type of cycle were the only one

acting. Call these values

123

, , NN N, etc.

3) For each type of stress cycle, calculate the usage factors

U ,

U etc., from

111 2 22 3 33

,,UnNUnNUnN== =, or for the ith cycle:

(4.19.1)

4) Calculate the cumulative usage factor

U by summing the individual factors, or

123

...

UU U U U=++++.

5) The cumulative usage factor

U for the total number of stress cycles, m , shall not exceed 1.0, or

1.0

=≤

∑∑

(4.19.2)

b) Fatigue Correlation Testing – In complying with the requirements of paragraph 4.19.5.7 (unreinforced

bellows), paragraph 4.19.6.7 (reinforced bellows), or paragraph 4.19.7.7 (toroidal bellows) the

calculation and relation to fatigue life may be performed by any method based on the theory of elasticity.

However, the method must be substantiated by correlation with proof or strain gage testing (see Annex

5.E) on a consistent series of bellows of the same basic design (annealed, and as formed bellows are

considered as separate designs) by the bellows Manufacturer to demonstrate predictability of rupture

pressure and cyclic life.

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1) The substantiation of any analytical procedure shall be based on data obtained from five separate

tests on bellows of the same basic design. When substantiating bellows designs with more than

two convolutions in series, the test data shall have been obtained from bellows with a minimum of

three convolutions.

2) When compared with the data obtained from the calculation procedure, the test data shall

demonstrate that the rupture pressure of the bellows is equal to or greater than three times the

maximum allowable working pressure at room temperature.

3) When

S along with the other appropriate factors are used in the cycle life equations in paragraph

4.19.5.7 (unreinforced bellows), paragraph 4.19.6.7 (reinforced bellows), or paragraph 4.19.7.7

(toroidal bellows), the required design life

alw

N shall be less than the calculated cycles to failure

based on the data obtained by testing. The design cycle life may not be increased above that

obtained from the equations in these paragraphs regardless of the test results. The substantiation

of analytical procedures shall be available for review by the Inspector.

4.19.4 Materials

Pressure-restraining component materials including the restraining elements covered by paragraph 4.19.3.1.c

shall comply with the requirements of Part 3.

4.19.5 Design of U-Shaped Unreinforced Bellows

4.19.5.1 Scope

These rules cover the design of bellows having unreinforced U-shaped convolutions. Each half convolution

consists of a sidewall and two tori of nearly the same radius (at the crest and root of the convolution), in the

neutral position, so that the convolution profile presents a smooth geometrical shape as shown in Figure

4.19.1 Sketch (a).

4.19.5.2 Conditions of Applicability

The following conditions of applicability apply in addition to those listed in paragraph 4.19.2.

a) A variation of 10% between the crest convolution radius

r and the root convolution radius

r is

permitted (see Figure 4.19.2)

b) The torus radius shall be such that:

rt≥ , where: ()2

iicir

rrr

+ ,

c) The off-set angle of the sidewalls,

, in the neutral position shall be such that: 15 15

−≤≤+

degrees (see Figure 4.19.2). In this case,

q is defined as the length between two consecutive

convolutions when their sidewalls have been made parallel.

d) The convolution height shall be such that:

≤

4.19.5.3 Internal Pressure

The required stress calculations and acceptance criteria for U-shaped unreinforced bellows are given in

Table 4.19.1.

4.19.5.4 Column Instability Due to Internal Pressure

a) The allowable internal design pressure to avoid column instability is given by the following equation.

0.34

= (4.19.3)

b) The internal pressure shall satisfy the following equation.

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PP≤ (4.19.4)

4.19.5.5 In-Plane Instability Due to Internal Pressure

a) The allowable internal design pressure based on in-plane instability is given by the following equation.

()

0.5

224

12 12 4

δδδ

−

⎡⎤

++−+

⎢⎥

⎣⎦

(4.19.5)

where

(4.19.6)

S is the effective yield strength at design temperature (unless otherwise specified) of bellows material

in the as-formed or annealed condition. If

S is not available in material standards, the values shown in

the following equations shall be used where

S is the yield strength of bellows material at design

temperature, given by Annex 3.D. Higher values of

S may be used if justified by representative tests.

2.3

S S for as formed bellows=− (4.19.7)

0.75

S S for annealed bellows=

(4.19.8)

c) The internal pressure shall satisfy the following equation.

PP≤ (4.19.9)

4.19.5.6 External Pressure Strength

a) External pressure capacity – The rules of paragraph 4.19.5.3 shall be applied taking P as the absolute

value of the external pressure. When the expansion bellows is subjected to vacuum, the design shall be

performed assuming that only the internal ply resists the pressure. The pressure stress equations of

paragraph 4.19.5.3 shall be applied with

b) Instability due to external pressure – The design shall be performed according to the rules of paragraph

4.4 by replacing the bellows with an equivalent cylinder, using an equivalent outside diameter,

D , and

an equivalent thickness,

, given by the following equations where

is the moment of inertia (see

Figure 4.19.3).

eq b eq

DDwe=++ (4.19.10)

()

1/3

12 1

⎛⎞

−

⎜⎟

⎝⎠

(4.19.11)

c) If

0L = ,

is given by the following equation.

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()

0.4 0.2

xx p

nt q w q

⎡⎤

−

=+−

⎢⎥

⎣⎦

(4.19.12)

4.19.5.7 Fatigue Evaluation

a) The meridional membrane and bending stresses due to the total equivalent axial displacement range

qΔ

of each convolution is given by the following equations.

Et q

(4.19.13)

Et q

(4.19.14)

C and

C are evaluated using Tables 4.19.3 and 4.19.4, respectively.

b) The total stress range due to cyclic displacement is given by the following equation.

[

]

[

]

34 56

0.7

SSSSS=+++ (4.19.15)

c) Calculation of allowable number of cycles

1) The specified number of cycles

shall be specified in consideration of the anticipated number

of cycles expected to occur during the operating life of the bellows. The allowable number of cycles

shall satisfy the following equation.

alw spe

NN≥

(4.19.16)

2) The allowable number of cycles,

alw

N , shall be calculated using the equations in Table 4.19.5.

These equations are valid for:

i) Austenitic chromium-nickel stainless steels, UNS N066XX and UNS N04400 for metal

temperatures not exceeding 425°C (800°F).

ii) U-shaped unreinforced bellows, as-formed or annealed

3) If the bellows is subjected to different cycles of pressure or displacement, such as those produced

by start-up or shutdown, their cumulative damage shall be considered as in paragraph 4.19.3.2.a.

4) For fatigue correlation testing, see paragraph 4.19.3.2.b.

4.19.5.8 Axial Stiffness

The theoretical axial stiffness of a bellows comprised of

N convolutions may be evaluated by the following

equation. This equation is valid only in the elastic range. Outside of the elastic range lower values can be

used, based upon Manufacturer's experience or representative test results.

()

E D

⎛⎞

⎜⎟

−

⎝⎠

(4.19.17)

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4.19.6 Design of U-Shaped Reinforced Bellows

4.19.6.1 Scope

These rules cover the design of bellows having U-shaped convolutions with rings to reinforce the bellows

against internal pressure. Each half convolution consists of a sidewall and two tori of nearly the same radius

(at the crest and root of the convolution), in the neutral position, so that the convolution profile presents a

smooth geometrical shape as shown in Figure 4.19.1 Sketch (b).

4.19.6.2 Conditions of Applicability

The conditions of applicability are given in paragraph 4.19.5.2.

4.19.6.3 Internal Pressure

The required stress calculations and acceptance criteria for U-shaped reinforced bellows are given in Table

4.19.6.

4.19.6.4 Column Instability Due to Internal Pressure

a) The allowable internal design pressure to avoid column instability is given by the following equation.

0.3

= (4.19.18)

b) The internal pressure shall satisfy the following equation.

PP≤ (4.19.19)

4.19.6.5 In-Plane Instability Due to Internal Pressure

Reinforced bellows are not prone to in-plane instability.

4.19.6.6 External Pressure Strength

a) External pressure capacity – The rules of paragraph 4.19.5.3 relative to unreinforced bellows shall be

applied taking P as the absolute value of the external pressure. When the expansion bellows is

subjected to vacuum, the design shall be performed assuming that only the internal ply resists the

pressure. The pressure stress equations of paragraph 4.19.5.3 shall be applied with

1n = .

b) Instability due to external pressure – The circumferential instability of a reinforced bellows shall be

calculated in the same manner as for unreinforced bellows (see paragraph 4.19.5.6.b)

4.19.6.7 Fatigue Evaluation

a) The meridional membrane and bending stresses due to the total equivalent axial displacement range

qΔ of each convolution are given by the following equations.

()

Et q

wCqC

−

(4.19.20)

()

Et q

wCqC

−

(4.19.21)

C and

C are evaluated using Tables 4.19.3 and 4.19.4, respectively.

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b) The total stress range due to cyclic displacement is given by Equation (4.19.15).

The fatigue evaluation of a reinforced bellows shall be calculated in the same manner as for

unreinforced bellows (see paragraph 4.19.5.7.c), except that the allowable number of cycles shall be

calculated using the equations in Table 4.19.7.

4.19.6.8 Axial Stiffness

The theoretical axial stiffness of a bellows comprised of

N convolutions is given by the following equation.

()

E D

NwCq

⎛⎞

⎜⎟

−

⎝⎠

(4.19.22)

This equation is valid only in the elastic range. Outside of the elastic range lower values can be used, based

upon Manufacturer's experience or representative test results.

4.19.7 Design of Toroidal Bellows

4.19.7.1 Scope

These rules cover the design of bellows having toroidal convolutions. Each convolution consists of a torus of

radius

r as shown in Figure 4.19.1 Sketch (c).

4.19.7.2 Conditions of Applicability

The conditions of applicability are given in paragraph 4.19.2.

4.19.7.3 Internal Pressure

The required stress calculations and acceptance criteria for toroidal bellows are given in Table 4.19.8.

4.19.7.4 Column Instability Due to Internal Pressure

a) The allowable internal design pressure to avoid column instability is given by the following equation.

0.15

= (4.19.23)

b) The internal pressure shall satisfy the following equation.

PP≤ (4.19.24)

4.19.7.5 In-Plane Instability Due to Internal Pressure

Toroidal bellows are not prone to in-plane instability.

4.19.7.6 External Pressure Strength

a) External pressure capacity – The rules of paragraph 4.19.7.3 shall be applied taking P as the absolute

value of the external pressure and using

in the equations. When the expansion bellows is

subjected to vacuum, the design shall be performed assuming that only the internal ply resists the

pressure. The pressure stress equations of paragraph 4.19.7.3 shall be applied with

1n = .

b) Instability due to external pressure is not covered by the present rules.

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4.19.7.7 Fatigue Evaluation

a) The meridional membrane and bending stresses due to the total equivalent axial displacement range

qΔ

of each convolution are given by the following equations.

34.3

Et B q

(4.19.25)

5.72

Et B q

(4.19.26)

and

are evaluated using Table 4.19.9.

b) The total stress range due to cyclic displacement is given by the following equation.

356

SSSS=++ (4.19.27)

c) The fatigue evaluation of a toroidal bellows shall be calculated in the same manner as for unreinforced

bellows (see paragraph 4.19.5.7.c), except that the allowable number of cycles shall be calculated using

the equations in Table 4.19.10.

4.19.7.8 Axial Stiffness

The theoretical axial stiffness of a bellows comprised of

convolutions is given by the following equation.

12 (1 )

EDB

⎛⎞

⎜⎟

−

⎝⎠

(4.19.28)

is evaluated using Table 4.19.9. This equation is valid only in the elastic range. Outside of the elastic

range lower values can be used, based upon Manufacturer's experience or representative test results.

4.19.8 Bellows Subject to Axial, Lateral or Angular Displacements

4.19.8.1 General

The purpose of this paragraph is to determine the equivalent axial displacement of an expansion bellows

subjected at its ends to:

a) an axial displacement from the neutral position:

in extension

(

)

0x > or in compression

()

b) a lateral deflection from the neutral position:

(

)

0y >

c) an angular rotation from the neutral position:

(

)

4.19.8.2 Axial displacement

a) When the ends of the bellows are subjected to an axial displacement

(see Figure 4.19.4), the

equivalent axial displacement per convolution is given by the following equation. In this equation,

shall be taken as positive for extension

(

)

0x > and negative for compression

()

0x < . Values of

extension and compression may be different.

Δ= (4.19.29)

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