APPENDIX 26 PRESSURE VESSEL AND HEAT EXCHANGER … · APPENDIX 26 PRESSURE VESSEL AND HEAT EXCHANGER EXPANSION JOINTS 26-1 GENERAL (a) Expansion joints used as an integral part of

APPENDIX 26PRESSURE VESSEL AND HEAT EXCHANGER

EXPANSION JOINTS

26-1 GENERAL

(a) Expansion joints used as an integral part of heatexchangers or other pressure vessels shall be designedto provide flexibility for thermal expansion and alsoto function as a pressure containing element. The rulesin this Appendix are intended to apply to thin wall [t≤ 1⁄8 in. (3.2 mm)], single layer, bellows-type expansionjoint geometries, such as those shown in Fig. 26-1subject to internal pressure. The bellows shall consistof formed flexible elements with multiple or singleconvolutions and may be of the unreinforced or rein-forced type. The suitability of an expansion joint forthe specified design pressure, temperature, and deflectionshall be determined by the methods described herein.

This Appendix covers applications involving axialdeflection only. Angular and / or lateral deflection inher-ent in the fitup of the expansion joint to the pressurevessel is permissible provided the amount is specifiedand is included in the expansion joint design [see (c)below].

(b) In all vessels with integral expansion joints, thehydrostatic end force caused by pressure and / or thejoint spring force shall be resisted by adequate restraintelements (e.g., exchanger tubes or shell, external re-straints, anchors, etc.). The stress [see UG-23(c)] inthese restraining elements shall not exceed the maximumallowable stress at the design temperature for the mate-rial given in the tables referenced by UG-23.

(c) The joints shall be provided with bars or othersuitable members for maintaining the proper overalllength dimension during shipment and installation. Jointflexible elements shall not be extended, compressed,rotated, or laterally offset to accommodate connectingparts which are not properly aligned, unless the designconsiders such movements.

(d) The minimum thickness limitations of UG-16(b)and UHT-16(b) do not apply to bellows designed tothis Appendix. The normal thickness after forming foran unreinforced bellows-type expansion joint [see Fig.

469

26-1 sketch (a)] shall be calculated from the followingformula:

t ≥P (d + w)

S11.14 +4wq 2

The nominal thickness after forming for a reinforcedbellows-type expansion joint [see Fig. 26-1 sketch (b)]shall be calculated from the following formula:

t ≥P (d + w)

S11.14 +4wq 2

3 R(R + 1)4

The symbols defined below are used in the formulasof this Appendix [see Fig. 26-1].

tp nominal thickness of bellows after forming,in. (mm)

tp tm [d / (d + w)]1⁄2 relation between minimum

and nominal thicknesses accounting for thin-ning during forming, in. (mm)

tmp minimum thickness of bellows sheet materialbefore forming, in. (mm)

Pp internal design pressure (see UG-21), psi (kPa)dp inside diameter of bellows, in. (mm)Sp maximum allowable stress value, psi (kPa) (see

applicable table of stress values in SubsectionC)

wp convolution depth, in. (mm)qp convolution pitch, in. (mm)Rp ratio of internal pressure force resisted by the

bellows to that resisted by the reinforcement.Rfor two different types of reinforcing rings aregiven below asR1 andR2.

R1 is for continuous reinforcing rings withoutbolting:

R1 p AbEb / Ar Er

COPYRIGHT American Society of Mechanical EngineersLicensed by Information Handling ServicesCOPYRIGHT American Society of Mechanical EngineersLicensed by Information Handling Services

Fig. 26-1 2001 SECTION VIII — DIVISION 1

FIG. 26-1 SOME TYPICAL BELLOWS TYPE EXPANSION JOINTS

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26-1 APPENDIX 26 — MANDATORY 26-1

tm

ts ts

d dWith groove weld

Weld end

Flexible element

Flexible element

GENERAL NOTES:(a)(b)

ts = minimum required component thickness plus corrosion allowance.Nominal r 3tm.

tm

r

Flexible element

Weld end

With groove weldGroove or

fillet weldGroove or fillet weld

ts

r min. = 1/8 in. (3.2 mm)r min. = 1/8 in. (3.2 mm)

ts

d

tm

r

Bolted or welded collar

Groove or fillet weld

r min. = 1/8 in. (3.2 mm)

1/4 in. (6 mm) max.

r min. = 1/8 in. (3.2 mm)

FIG. 26-2 SOME TYPICAL FLEXIBLE ELEMENT TO WELD END DETAILS

R2 is for noncontinuous reinforcing rings withbolting:

R2 p 1 AbEb

d + w2 1 ,f

Af Ef+

d + wAr Er 2

Abp (0.571q + 2w)t cross-sectional metal area ofone convolution wheret is determined fromthe minimum thicknesstm of the sheet materialbefore forming, in.2 (mm2)

Ar p minimum cross-sectional metal area of one rein-forcing ring, in.2 (mm2)

471

Af p minimum cross-sectional root area of one fas-tener bolt, in.2 (mm2)

,f p effective length of one bolt, in. (mm)Ep modulus of elasticity at design temperature per

Table UF-27, psi (kPa) (subscripts denote:b,bellow; f, fastener;r, reinforcing rings)

E′bp modulus of elasticity at room temperature, psi(kPa)

Cpp factor from Fig. 26-3Cfp factor from Fig. 26-4Cdp factor from Fig. 26-5

ep design axial movement of joint per convolution,in. (mm)



FIG. 26-3 Cp FACTOR

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APPENDIX 26 — MANDATORY Fig. 26-4

FIG. 26-4 Cf FACTOR

473



FIG. 26-5 Cd FACTOR

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kp 0.3 − 1 1000.6P1.5 + 3202

2

for Customary units

kp 0.3 − 1 17980.6P1.5 + 575 3602

2

for SI units

(e) As stated in U-2(g), this Division does not containrules to cover all details of design and construction.The criteria in this Appendix are, therefore, establishedto cover some common expansion joint types, but itis not intended to limit configurations or details tothose illustrated or otherwise described herein. However,when evaluating designs which differ from the basicconcepts of this Appendix (e.g., multilayer, asymmetricgeometries or loadings, external pressure, etc.), thedesign shall comply with the requirements of U-2(g).

26-2 MATERIALS

Pressure-retaining component materials including therestraint elements covered by 26-1(b) shall conform tothe requirements of UG-4.

26-3 DESIGN

The design of expansion joints shall conform to therequirements of Part UG and those of (a) through (g)below.

(a) The design of expansion joint flexible elementsshall consider the following combinations of maximumstress components and the corresponding stress limits:

Scmp ≤ S (1)

Smmp ≤ S (2)

Smmp + Smbp ≤ KS (3)

0.7 (Smmp+ Smbp) + Smmd+ Smbd p Sn [see (c) below] (4)

whereScmpp circumferential membrane stress due to internal

pressure, psi (kPa)Smmpp meridional membrane stress due to internal

pressure, psi (kPa)Smbpp meridional bending stress due to internal pres-

sure, psi (kPa)

475

Smmdp meridional membrane stress due to deflection,psi (kPa)

Smbdp meridional bending stress due to deflection,psi (kPa)

The above stresses shall be determined using athickness t which accounts for the thinning duringforming.

Sp maximum allowable stress value, psi (kPa) (seeapplicable table of stress values referenced inUG-23)

Kp 1.5 for unreinforced bellows. Alternative factorsmay be used if substantiated by test data (e.g.,by hydrotest for design temperatures below thecreep range). However, the factor shall be nogreater than 3.0.

Kp 3.0 for reinforced bellowsSnp maximum combined meridional membrane and

bending stress range in a flexible element dueto the cyclic components of pressure and de-flection, psi (kPa). The calculation of the indi-vidual stress components and their combinationshall be determined using the methods of elasticstress analysis as outlined in (c) below.

(b) The required joint design lifeN in cycles shall beestablished by the designer considering the anticipatednumber of stress cycles (pressure and / or deflection)expected to occur during the operating life of the unit,but in no case shall it be less than 100. Factors havebeen included in the following cycle life equations toaccount for the normal effects of size, annealing, surfacefinish, and scatter of data. Therefore, the required cyclelife should be established to realistically represent theestimated number of operating cycles. An overly conser-vative estimate of cycles can result in a greater numberof convolutions and a joint which is more prone toinstability [see (d) below]. The suitability of an expan-sion joint to withstand the required number of cyclesshall be determined from one of the following equations,depending on its material of construction.

For unreinforced bellows with≤ 40,000 cycle life:

N ≤ 1 2.7214.78Kg Sn

Eb− 0.022

2.0

, cycles

For unreinforced bellows with> 40,000 cycle life:

N ≤ 1 4.3818.50Kg Sn

Eb− 0.022

2.0

, cycles


26-3 2001 SECTION VIII — DIVISION 1 26-3

For reinforced bellows with≤ 40,000 cycle life:

N ≤ 1 2.7211.67Kg Sn

Eb− 0.022

2.0

, cycles

For reinforced bellows with> 40,000 cycle life:

N ≤ 1 4.3814.59Kg Sn

Eb− 0.022

2.0

, cycles

for series 3XX high alloy steels and for nickel alloysUNS N04400, UNS N06600, UNS N06625, UNSN08800, UNS N08810, and UNS N08811 for metaltemperatures not exceeding 800°F (427°C).1

For unreinforced bellows with> 40,000 cycle life, when

18.50Kg Sn

Eb≤ 0.024,

or for renforced bellows with> 40,000 cycle life, when

14.59Kg Sn

Eb≤ 0.024,

then the expansion joint is limited to 106 cycles.

In the above formulas,Kgp fatigue strength reduction factor which accounts

for geometrical stress concentration factors dueto thickness variations, weld geometries, sur-face notches, and other surface or environmentalconditions. The rangeKg is 1.0≤ Kg ≤ 4.0 withits minimum value for smooth geometricalshapes and its maximum for 90 deg. weldedcorners and fillet welds. Fatigue strength reduc-tion factors may be determined from theoretical,experimental, or photoelastic studies. A factorhas already been included in the above equa-tions forN to account for normal effects of size,environment, and surface finish. For bellows-type expansion joints without circumferentialwelds and meeting all the design and examina-tion requirements of this Appendix, aKg of 1.0may be used.

Ebp modulus of elasticity at design temperature, psi(kPa) (see Table UF-27)

1 Temperatures may be exceeded if substantiated by elevated tempera-ture fatigue test data or design curves [see 26-3(d)]; otherwise, therequirements of U-2(g) shall apply.

476

(c) In complying with the requirements of (a) and(b) above, the calculation and relation to fatigue lifemay be performed by any method based on the theoryof elasticity. However, the method must be substantiatedby correlation with proof or strain gage testing (UG-101) on a consistent series of flexible elements of thesame basic design (unreinforced, reinforced, annealed,and as formed are considered as separate designs) bythe manufacturer to demonstrate predictability of rupturepressure and cyclic life. The substantiation of anyanalytical procedure shall be based on data obtainedfrom five separate tests on flexible elements of thesame basic design. When substantiating expansion jointdesigns with more than two convolutions in series, thetest data shall have been obtained from joints with aminimum of three convolutions. When compared withthe data obtained from the calculation procedure, thetest data shall demonstrate that the rupture pressure ofthe flexible elements is equal to or greater than threetimes the maximum allowable working pressure at roomtemperature. WhenSn along with the other appropriatefactors are used in the cycle life equations in (b) above,the required design lifeN shall be less than the calculatedcycles to failure based on the data obtained by testing.Design cycle life may not be increased above thatobtained from the equations in (b) above regardless ofthe test results. The substantiation of analytical proce-dures shall be available for review by the Inspector.

(d) Bellows-type expansion joints in Fig. 26-1sketches (a) and (b) may become unstable (squirm)when located by internal pressure and axial deflection.Therefore, the manufacturer shall test the ability of thebellows to withstand a pressure test as required in 26-6 without excessive squirm. Expansion joints withcumulative bellows length to diameter,L / d (see Fig.26-1) ratio greater than 1.0 shall show by calculationor testing that a minimum factor of 2.25 exists betweenthe equivalent maximum allowable working pressureat room temperature and the internal pressure at whichthe bellows will become unstable (column squirm). Bydefinition, squirm shall be considered to have occurredif under the internal test pressure an initially symmetricalbellows deforms, resulting in a lack of parallelism oran uneven spacing of adjacent convolutions at anypoint on the circumference which can be observedvisually. This deformation shall be considered as exces-sive squirm when the ratio of the maximum bellowspitch under internal pressure to the bellows pitch beforeapplication of pressure exceeds 1.15 for unreinforcedand 1.20 for reinforced bellows.

(e) The knuckle radiusr of any formed elementshall not be less than 3 times the thicknesstm as shown

01



in Fig. 26-1 unless the increased bending stress dueto curvature is accounted for in the correlation testingof (b) above.

(f) The spring rate, lb / in. (kN / m), of the expansionjoint assembly may be determined by calculation orby testing.

(g) Longitudinal weld seams that comply with 26-4 and 26-5 shall be considered to have a joint efficiencyof 1.00.

(h) The following are design equations for bellows-type expansion joints which may be used for the designof such joints. However, use of these equations doesnot preclude satisfying the substantiation testing requiredby (c) above.

(1) Design Equations for Unreinforced Bellows

Bellows circumferential membrane stress due to internalpressure:

Scmp pP(d + w)

t11.14 +4wq 2

Bellows meridional membrane stress due to internalpressure:

Smmp pPw2t

Bellows meridional bending stress due to internal pres-sure:

Smbp pPw2Cp

2t2

Bellows meridional membrane stress due to deflection:

Smmd pE′bt2e

2w3Cf

Bellows meridional bending stress due to deflection:

Smbd p5E′bte

3w2Cd

(2) Design Equations for Reinforced Bellows

Bellows circumferential membrane stress due to internalpressure:

Scmp pP(d + w)

t11.14 +4wq 2

1 RR + 12

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NOTE: In the case of reinforcing members which are made insections and joined by fasteners in tension, this equation assumesthat the structure used to retain the fastener does not bend so as topermit the reinforcing member to expand diametrically. In addition,reinforcing members on each end of the bellows must be restrainedagainst the longitudinal annular pressure load of the bellows.

Reinforcing member circumferential membrane stressdue to internal pressure:

SRcmp pPq(d + w)

2Ar 1 1R1 + 12

Reinforcing member bolting stress in circumferentialdirection due to internal pressure:

SBcmp pPq(d + w)

2Af 1 1R2 + 12

NOTE: In the case of equalizing rings, this equation provides onlythe membrane stress and does not account for any bending stresscaused by an eccentric fastener location. These stresses can bedetermined by elastic analysis and / or testing.

Bellows meridional membrane stress due to internalpressure:

Smmp pP(w − kq)

2t

Bellows meridional bending stress due to internal pres-sure:

Smbp pP2 1w − kq

t 22

Cp

Bellows meridional membrane stress due to deflection:

Smmd pE′b t2e

2(w − kq)3Cf

Bellows meridional bending stress due to deflection:

Smbd p5E′bte

3(w − kq)2Cd

26-4 FABRICATION

The following requirements shall be met in thefabrication of expansion joint flexible elements.

(a) All welded joints shall comply with the require-ments of UW-26 through UW-36.

(b) All longitudinal weld seams shall be butt-typefull penetration welds; Type (1) of Table UW-12.


01


(c) Bellows-type flexible elements shall be attachedto the weld end elements by circumferential butt orfull fillet welds as shown in Fig. 26-2.

(d) Other than the attachment welds, no circumferen-tial welds are permitted in the fabrication of bellows-type flexible elements unless they are accounted for inthe determination ofKg [see 26-3(b)].

26-5 EXAMINATION

The following examinations are required to verifythe integrity of expansion joints.

(a) All expansion joint flexible elements shall bevisually examined for and shall be free of injuriousdefects, such as notches, crevices, material buildup orupsetting, weld spatter, etc., which may serve as pointsof local stress concentrations. Suspect surface areasshall be further examined by liquid penetrant or mag-netic particle examination.

(b) All full penetration butt-type welds shall be exam-ined 100% on the inside and outside surfaces by theliquid penetrant or magnetic particle methods beforeforming. This examination shall be repeated after form-ing to the maximum extent possible considering thephysical and visual access to the weld surfaces afterforming.

(c) The circumferential attachment welds betweenthe bellows and the weld ends shall be examined100% by the liquid penetrant or magnetic particleexaminations.

(d) Liquid penetrant examination shall be per Appen-dix 8 and magnetic particle examination shall be perAppendix 6. However, any linear indication found byexamination shall be considered relevant if the dimen-sion exceedstm / 4, but not less than 0.010 in. (0.25 mm),wheretm is the minimum bellows wall thickness beforeforming in inches.

26-6 PRESSURE TEST REQUIREMENTS

The pressure testing requirements for expansion jointsshall be as follows.

(a) The completed expansion joint shall be subjectedto a pressure test in accordance with UG-99 or UG-100. The pressure testing of an expansion joint maybe performed as a part of the vessel pressure test,provided the joint is accessible for inspection duringpressure testing.

(b) In addition to inspecting the expansion joint forleaks and general structural integrity during the pressuretest, an expansion joint shall be inspected before, during,

478

and after the pressure test to confirm that the require-ments of 26-3(d) are satisfied.

(c) Any expansion joint restraining elements [see 26-1(b)] shall also be pressure tested in accordance withUG-99 or UG-100 as a part of the initial expansionjoint pressure test, or as a part of the final vesselpressure test after installation of the joint.

26-7 MARKING AND REPORTS

When the expansion joint is manufactured by otherthan the vessel Manufacturer, the Manufacturer of theexpansion joint shall have a valid ASME Code UCertificate of Authorization and shall complete a FormU-2 or Form U-2A Manufacturers’ Partial Data Reportas required by UG-120(c). A copy of this Partial DataReport shall be attached to and become part of theForm U-1 or Form U-1A Manufacturers’ Data Reportfor the completed vessel.

(a) The Manufacturers’ Data Report shall includethe following additional data and statements:

(1) maximum allowable working pressurepsi at °F; minimum design metal

temperature °F at pressure of psi;(2) spring rate, axial movement, and loading condi-

tions for which the expansion joint is designed;(3) service conditions or restrictions;(4) design life cycles;(5) the Partial Data Report in addition to recording

the Manufacturer’s serial number shall identify thevessel Manufacturer and the specific design for whichthe expansion joint is intended;

(6) that the joint has been constructed to the rulesof this Appendix.

(b) The part Manufacturer shall identify the expan-sion joint with the following:

(1) name of part Manufacturer;(2) serial number;(3) maximum allowable working pressure

psi at °F; minimum design metaltemperature °F at pressure of psi;

(4) ASME U Symbol stamp above the wordPart,as required by UG-116(i).

(c) Identification stamping or other Code markingshall not be located on the formed flexible elementsof the expansion joint.

26-8 EXAMPLES

Examples illustrating use of the rules of this Appendixare as follows.



(a) An unreinforced bellows-type expansion jointconsists of 8 convolutions, formed from 0.05 in. thicksheettm, inside diameterd of 24 in., convolution depthw of 1 in., cumulative bellows lengthL of 9 in.,fabricated from SA-240 TP304 stainless steel, internaldesign pressure of 150 psi, design temperature of 200°F,required cycle lifeN of 1000 cycles, and total jointaxial movement of 1 in. (1⁄8 in. per convolutione).Does this joint satisfy the rules of this Appendix?Check for adequacy of minimum sheet thickness beforeforming per 26-1(d):

t pP(d + w)

S11.14 +4wq 2

and

tmp t 1d + wd 2

0.5

Sp 17,800 psidp 24 in.wp 1 in.qp L / number of convolutionsp 9 in. / 8 p 1.125 in.

Ebp 27.7 × 106 psiE ′bp 28.3 × 106 psi

t p150(24 + 1)

17,80011.14 +4(1)

1.1252p 0.045 in.

and

tm p 0.0451 25242

0.5

p 0.046 in.

The 0.05 in. thick sheettm specified is acceptable.Check 26-3(e) knuckle (r ≥ 3t) radius 3t limit:

r pq4

−tm2

p1.125

4−

0.052

p 0.256

p 0.256 in.≥ 3(0.05)

Check 26-3(d)L / d limit for squirm considerations:9 / 24 < 1.0.DetermineSmmp, Smmd, andSmbdper 26-3(c), and evaluate

479

results with 26-3(a) criteria withS p 17,800 psi andK p 1.5.

Smmp p 1500< 17,800

Smbp p 19,700

Smmp + Smbp p 21,200< 26,700

Smmd p 2600

Smbd p163,000

DetermineSn per 26-3(a) using cyclic componentsof stress which in this example are both pressure anddeflection:

Sn p 0.7(1500 + 19,700) + 2600 + 163,000

p 180,440 psi

Calculate expansion joint design cycle life from 26-3(b):

N p 1000≤ 1 2.7214.78KgSn

Eb− 0.02 2

2.0

Expansion joint is smooth formed stainless steeljoint without any significant notches at welds or otherlocations and, therefore,Kg p 1.0:

N p 1000≤ 1 2.7214.78(1)(180,440)

27.7 × 106− 0.02 2

2.0

p 1272 cycles

which is greater than the requiredcycle life of 1000.(b) A reinforced bellows-type expansion joint consists

of 6 convolutions, formed from 0.06 in. thick sheettm, inside diameterd of 24 in., convolution depthwof 1.25 in., cumulative bellows lengthL of 6.75 in.,with solid 0.5 in. diameter reinforcing rings, all fabri-cated from SA-240 TP304 stainless steel, design pres-sure of 450 psi, design temperature of 200°F, requiredcycle lifeN of 500 cycles, and total joint axial movementof 0.6 in. (0.1 in. per convolutione). Does this jointsatisfy the rules of this Appendix?


01


Check for nominal thickness after forming per 26-1(d):

t pP(d + w)

S11.14 +4wq 2

1 RR + 12

and

tm p t 1d + wd 2

0.5

Sp 17,800 psidp 24 in.wp 1.25 in.qp L / number of convolutionsp 6.75 in. / 6p 1.125 in.

Rp AbEb / ArEr

Ebp Er p 27.7 × 106 psiE ′bp 28.3 × 106 psiAbp (0.571q + 2w)t

p [0.571(1.125) + 2(1.25)] (0.058)p 0.182

Ar p pr 2 p p(0.25)2 p 0.196 in.2

Rp(0.182)(27.7)(0.196)(27.7)

p 0.93

t p450(24 + 1.25)

17,80011.14 +4(1.25)1.1252

10.931.932 p 0.055

tm p 0.055125.2524 2

0.5

p 0.056 in.

The 0.06 in. thickness specified is acceptable.Check 26-3(c) knuckle (r > 3tm) radius limit:

r pq4

−tm2

p1.125

4−

0.062

p 0.25

p 0.25 in.> 3(0.06)

Check stresses in reinforcing ring:

Ar pp(0.5)2

4p 0.196

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SRcmp pPq(d + w)

2 Ar 1 1R1 + 12

SRcmp p450(1.125)(24 + 1.25)

2(0.196) 1 11.932

SRcmp p 16,870 psi which is less than the 17,800 psiallowable stress for the ring material.DetermineSmmp, Smbp, Smmd, and Smbd per 26-3(c), andevaluate results with 26-3(a) criteria withS p 17,800psi, K p 3.0.

Smmp p 3500< 17,800

Smbp p 38,400

Smmp + Smbp p 41,900< 53,400

Smmd p 3700

Smbd p 200,000

DetermineSn per 26-3(a) using cyclic componentsof stress which in this example are both pressure anddeflection:

Sn p Smmp + Smbp + Smmd p Smbd

p 3500 + 38,400 + 3700 + 200,000

p 245,600 psi

Calculate expansion joint design cycle life from 26-3(b):

N p 500 ≤ 1 2.514.2KgSn

Eb− 0.022

2.0

Expansion joint is smooth formed stainless steeljoint without any significant notches at welds or otherlocations and, therefore,Kg p 1.0.

N p 500

≤ 1 2.514.2(1)(245,600)

27.7 × 106− 0.02 2

2.0

p 557 cycles

which is greater than the required cycle life of 500.


Documents

APPENDIX 26 PRESSURE VESSEL AND HEAT EXCHANGER … · APPENDIX 26 PRESSURE VESSEL AND HEAT EXCHANGER EXPANSION JOINTS 26-1 GENERAL (a) Expansion joints used as an integral part of