valve clamp stress analysis

Valve Clamp Ring Stress Analysis

V-Rep 79-4

2

Valve Clamp Ring Stress AnalysisAbstractThe role of a clamp ring joint for use on avalve is defined. The results of elastic jointtheory are used to show the importance ofthe relative stiffnesses of the joint membersin determining the load in the clamp ring.A conventional approach to the design ofthe central portion of a clamp ring usingprimary stress equations is discussed, fol-lowed by an axisymmetric finite elementanalysis which establishes the maximumload capacity without yielding of a conven-tionally designed clamp ring. Further, elas-tic-plastic finite element analysis shows thatsubstantial overload capacity existsthrough plastic deformation. Finally, clampring body axial stress from the finite ele-ment analysis is compared to that from anequation in Appendix Z to Section VIII ofthe ASME B&PV Code and demonstratesthe conservatism of that equation.

NomenclatureC1 = clearance between the yoke

outside radius and the clamp lipinside radius

C2 = clearance between the hub outsideradius and the clamp body insideradius

h = overall clamp ring height in axialdirection

He = external axial load on clamp ringjoint

Hp = axial preload due to bolting onclamp ring

Hr = resultant or design axial clampring load

kc = stiffness of clamp ringkh = combined stiffness of clamped

hubs P = valve actuator load r1 = clamp lip inside radius ra = hub outside radius rh = hub/clamp ring contact surface

outside radiusri = clamp inside radius ry = yoke outside radius ta = clamp body thickness ts - clamp lip shear thickness m - friction angle at hub/clamp

contact surface slope angle ofhub/clamp contact surface

f = slope angle of hub/clamp contactsurface

IntroductionA clamp or lock ring performs the functionof clamping together axially-adjacent,axisymmetric structures through the conver-sion of circumferential bolt load to an axialclamp load. The connection of the commonstreet fire hydrant to the upright line fromthe supply main under the street is madefrequently with a clamp ring and may be afamiliar example. Clamp rings are used tojoin pipes, pipes and fittings and majorvalve components, which is the usedescribed in this paper.Two clamp ring joints are shown on thevalve in Figure 1; the upper clamp ringjoins the actuator to the yoke and thelower clamp ring joins the yoke to thevalve body. A typical clamp ring assemblyis shown in Figure 2 and consists of two C-shaped segments positioned end-to-endand bolting. A section through the centralportion of a clamp ring and the clampedhubs of the members to be connected isdepicted in Figure 3. During joint assem-bly, the bolts are tightened (preloaded),which causes the clamp ring to be drawnin radially and to develop an axial clamppreload on the hubs through the wedgingaction of the sloped clamp ring/hub con-tact surfaces. The gap between the clamplugs (see Figure 2) prevents lug-to-lug con-tact as the bolts are tightened, contactwhich would prevent effective conversionof bolt load to clamp load.

byM. J. KirikSupervisory Research Engineer, Applied MechanicsValve Engineering and Research, FlowControl DivisionRockwell InternationalFirst Published 1979

3

Several aspects of clamp ring stress analy-sis are covered in this paper: transfer ofloads to the ring, a conventional method ofclamp ring design, finite element analysisof a conventionally designed clamp ringand comparison of a finite element modelstress to an ASME B&PV Code equationvalue.Just the central portion of a clamp ring seg-ment (between the clamp lugs) is consid-ered. The clamp lugs and bolting are omit-ted because their stress analyses are essen-tially straight-forward.In stress analysis or design it is importantto have accurate knowledge of the loadingon a structure. Therefore, loading situationsfor a valve clamp ring joint will be coveredalong with the factors affecting transfer ofjoint loads to the clamp ring.It will be shown that the basic dimensionsof the clamp ring section in Figure 3 canbe established using a conventional designapproach based on the valve actuatorload acting to separate the joint, equilibri-um equations for certain average primarystresses and stress limits which experiencehas shown to be adequately conservative.This is a quick, routine method of clampring design.Occasionally, a clamp ring of conventionaldesign must be considered for an applica-tion where the clamp load is greater thanthe design load. This can occur on a valverequiring an unusually high actuator loadfor valve operation or when seismic loadmust be considered. In such a situation the

finite element method can be used toestablish clamp ring adequacy by deter-mining the clamp load which initiatesyielding.Further, it will be shown by elastic-plasticfinite element analysis that the clamp ringhas substantial overload capacity beyondthe load which first causes yielding.Additional protection is thus providedagainst gross deformation or failure due tounanticipated loading.Finally, the equation from Appendix Z toSection VIII – Division 1 of the ASME B&PVCode for axial stress in the clamp body isbriefly discussed in comparison to the finiteelement result.


Figure 1: Use of clamp rings on a valve. Figure 2: Clamp ring configuration.

YOKE CLAMP RING

VALVE BODY

ACTUATOR

ACTUATORCLAMP RING

YOKECLAMP LUGS

CENTRALPORTION

4

Clamp LoadingA clamp ring joint is subjected to internalor self-contained loads that are caused bythe bolt preloading during joint assembly,and to external loads that are transmittedthrough the joint. An external load thatmust be carried through a valve clamp ringjoint is the actuator force exerted whenclosing a valve.In determining the design axial clamp ringload, Hr, acting at the clamp contact sur-faces, it is important to be aware of howan external load on the joint affects thebolt-induced preload in the clamp ring. Acommon misconception with regard to

clamped (or bolted) joints is that the pre-load in the clamp (or bolt) remainsunchanged when an external load isapplied to the joint, if that external load isnot greater than the preload. With this mis-understanding, it would be concluded thatthe maximum load to which the clamp ringis subjected is the clamp preload and,therefore, the preload would be taken asthe design clamp load. However, this is notthe case. Any external load acting in ten-sion on the preloaded joint will cause anincrease in clamp load beyond the preloadvalue. This increase will be a fraction ofthe external load and depend on the elas-tic properties of the joint members. Thesum of the preload and the fraction of theexternal load acting axially on the clampring should be used as the design axialclamp ring load.

PreloadPreloading the joint by tightening the boltsinduces loads of equal magnitude in theclamp and across the hubs. It can beshown that the bolt preload, Wp, neces-sary to produce an axial clamp preload,Hp, is expressed by (also see equation (3)in Appendix Z of the ASME B&PV Code):

where f is the slope angle of the contactsurface (10 degrees for the joint shown inFigure 3) and m is the friction angle (thearc-tangent of the coefficient of friction forthe contact surfaces). As the bolts are tight-ened, the clamp ring segments are usuallymalleted to reduce the effects of friction at

the contact surfaces. Because of this, acase can be made for assuming that thefriction angle is negligibly small comparedto the contact surface angle. On the otherhand, it is preferable to measure Hp andWp experimentally and infer a value for mfrom equation (1).As discussed in the following section onexternal loading, the value of the clampring/hub preload is usually taken equal inmagnitude to the maximum external jointload in tension. For a valve, this is normal-ly the actuator load, P, exerted while clos-ing the valve. Joint assembly practiceand/or experiments should establish thevalue of friction angle to be used in equa-tion (1) to obtain the bolt preload, Wp,necessary to develop a preload of Hp = Pin the clamp ring.

External LoadElastic joint analysis [1,2] reveals that anexternal load acting on a joint can have asignificant effect on the clamp preload andon the contact load at the hub-to-hub inter-face in the plane of section a-a in Figure3. If the external load acts to separate thejoint, as an actuator load would do for avalve closing operation, then the load inthe clamp ring increases beyond the pre-load value.This can be deduced from the equationbelow for total axial clamp ring load [1]:

where He is an external load acting on thejoint and kc and kh are the stiffnesses of


Figure 3: Cross section of central portion ofclamp ring and clamped hubs.

CLAMP LIP

b

a a

z

r

bYOKE HUB

BODY HUB

rh = 6.763 in.

ri = 6.935 in.

r1 = 6.495 in.

ts = 0.976 in.

ta = 0.973 in.

h = 4.31 in.

20°

10°

CLAMP

5

the clamp ring and the hubs, respectivelyThis equation indicates that a fraction ofany external joint load is always added tothe clamp ring preload.For the case where the axial component ofthe clamp ring preload, Hp, is set equal tothe actuator load for valve closing, P, andthis actuator load is also acting externallyon the joint, the resultant or maximumaxial clamp ring load, Hr, will be betweenP and 2P. When the stiffness of the hubs isgreater than the stiffness of the clamp ring,the resultant axial clamp ring load isbetween P and 1.5P; when the reverse istrue, the resultant axial clamp ring load isbetween 1.5P and 2P. For the joint shownin Figure 3, a theoretical estimate of theresultant axial clamp ring load is 1.5P andnot P, as would be expected if elastic jointeffects were not considered. Methods forestimating the stiffness of elastic joint com-ponents are given in [1,2].Thus it is important to consider the elastici-ty of the joint components in determiningthe maximum or design clamp load.Alternatively, a design clamp load of 2Pcan be used conservatively.Elastic joint analysis also reveals that thereason for setting the clamp preload equalto the actuator load value is that the jointwill not separate at the hub-to-hub interfacewhen the actuator load is applied to thejoint, regardless of the stiffnesses of thehubs and clamp ring. It can be shown thata separated joint has less stiffness than anon-separated joint, which may be ofsignificance depending on the application.A consequence of possible importance in

seismic analysis is that a structure with aclamp ring joint will have lower fundamen-tal natural frequency if the joint hubsseparate during the vibration cycle.Moreover, the frequency will be sensitiveto the amount of joint separation. Anotherconsideration is that a joint whichseparates can reduce fatigue life in acyclic load application.The preceding discussion on the effects ofexternal (actuator) load on the clamp pre-load ignores the influence of contactsurface friction. However, it is the author’sopinion that even with friction taken intoaccount the effects predicted by elasticjoint analysis should be substantiallysimilar. The main effect of friction at thecontact surface should be to restrict out-ward radial deflection of the clamp ringlips due to application of the external loadand thus reduce the amount of additionalload induced in the bolts and bendingstress in the clamp ring body. Ignoringfriction effects is, therefore, a conservativeapproach.

Conventional DesignOne approach to the design of clamprings is to limit certain average primarystresses and the bearing stress at thecontact surfaces, all due to the designaxial clamp ring load. The equation andrelations presented in this section aresufficient to obtain the basic dimensions ofa clamp ring.An examination of the clamp ring crosssection shown in Figure 3 would indicatethat there are two average primary stresseswhich must be limited to prevent excessive

yielding. One is the average axial stress atsection a-a (saa). Control of this stress pre-vents the ring from pulling apart. The sec-ond stress is the average shear stress onthe ring lip at section b-b (tbb) which islocated at the extremity of the hubs beingclamped. Control of this stress prevents theclamp lips from being sheared off. Anadditional stress to be considered is thecontact stress on the clamp lip (sc) due tothe clamping action on the hubs.All of these stresses are easily calculatedfrom static equilibrium with the designaxial clamp ring load and are expressedby:average axial stress at section a-a:

average shear stress at section b-b:

average contact stress on clamp lip:

Important stresses other than those men-tioned here occur in the clamp ring, butthese stresses are not calculable using sim-ple equations. An indirect approach to thecontrol of these stresses is to limit the aver-age stresses at sections a-a and b-b and atthe hub/clamp contact surface to low val-ues compared to the yield strength.An example of limits on stresses calculated


6

from equations (2), (3) and (4) thatexperience has shown to be satisfactoryfor valve clamp rings are: 5000, 5000and 20000 psi (34, 34 and 140 MPa),respectively, for SA 216, WCB carbonsteel. This is a common clamp ring materi-al in the valve industry and has a minimumyield strength of 36000 psi (250 MPa) atroom temperature [3].There are six basic design dimensionsshown for the clamp ring in Figure 3. Ofthese six dimensions, three must be chosento satisfy the stress limits previously men-tioned; the other three depend on theyoke, valve body and hub dimensions. Toillustrate this, a design approach might be:• Determine the maximum external joint

load (say the valve actuator load P).• Assume that the design axial clamp ring

load is Hr = 1.5P (or use a coefficientother than 1.5 consistent withexperience).

• Select a clearance C1, between the yokeoutside radius, ry (not indicated in Figure3) mind the clamp lip inside radius r1.Then:

r1 = ry + C1The clearance C1, must prevent clamplip contact with the yoke when the clampring is preloaded.

• Calculate the hub contact outside radius,rh, from equation (4) using the averagecontact stress limit.

• Calculate the clamp lip thickness, ts, atsection b-b from equation (3) using thesection b-b stress limit.

• Select a clearance C2, between the hub

outside radius, ra not indicated in Figure3), and the clamp inside radius ri. Then:

ri = ra + C2The clearance C2 must prevent clampring contact with the hub when theclamp ring is preloaded.

• Calculate the clamp thickness ta, fromequation (2) using the section a-a stresslimit.

• The overall axial clamp ring height, h,should be greater than the sum of thethickness of the hubs and the clamp lipthickness or about 4ts. This assumes thatthe hub thickness is the same as theclamp lip thickness in the axial directionat section b-b. Allowance in h must bemade beyond the minimum height (4ts)for the sloped surfaces and the outwardshape or appearance desired for theclamp ring.

• Check hub and clamp ring stiffnessesusing elastic joint analysis to verify thecoefficient used in the calculation of thedesign axial clamp ring load in the sec-ond step.

Design of clamp rings for a product line ofvalves on the just described conventionalbasis can be accomplished easily and eco-nomically. However, there is the problemin determining design adequacy for appli-cations where the axial clamp load isgreater than the design axial clamp ringload (Hr), considering the neglected stress-es in the clamp ring. As mentioned before,this situation can occur for seismic loadingon a valve of existing design or when con-templating the use of an existing clampring for a new application. A solution to

this problem is to perform a load test onthe clamp ring or use a finite elementanalysis to determine the maximum loadwithout significant yielding. The next sec-tion describes a finite element analysis per-formed on the clamp ring and the resultsobtained.

Finite Element AnalysisA finite element model of the clamp ringshown in Figure 3, pg. 4, was developedand loaded incrementally until a very smallportion of the ring yielded. This approxi-

Figure 4: Finite element model of clamp ringsection shown in Figure 3.

CLAMP LOAD

54


7

mately determined the margin between thedesign axial clamp ring load and the loadinitiating yielding. It is important that theclamp load which causes yielding beknown. Additional loading beyond thispoint produces permanent deformationand subsequently relaxes the clamp pre-load remaining when the additional clampload is removed.Loading was then increased arbitrarily bya factor of 1.5 to determine if significantdeformation occurred and the extent ofyielding in the clamp ring.Figure 4 shows the axisymmetric finite ele-ment model of a half-section of a clampring. Because the half-plane is a plane ofsymmetry, the finite element nodes thereare supported axially but free to moveradially. The clamp load is shown distrib-uted uniformly and normal to the surface.Friction effects at the contact surface areneglected.The CREEP-PLAST computer program wasused for this analysis. This program wasinitially distributed by the Oak RidgeNational Laboratory but is now handledby COSMIC (Computer SoftwareManagement and Information Center) atthe University of Georgia. Capabilities ofthe program include elastic-plastic-creepanalysis of two-dimensional plane oraxisymmetric structures. Further descriptionof the program may be found in [4 and [5]and an evaluation in [6].Material properties for this analysis arebased on a temperature of 400°F (200°C)which should be a representative servicecondition. CREEP-PLAST simulates the

stress-strain curve in a bilinear fashion asshown in Figure 5. The elastic modulus E is27 x 106 psi (190 GPa) and the yieldstress is 30800 psi (212 MPa) [3]. Theplastic modulus Ep is 1 x l06 psi (7GPa)and was calculated from a stress-straincurve for a SA 216, WCB carbon steel [7]for strains up to about 1 percent. Poisson’sratio is taken to be a nominal value of 0.3.Yielding is determined by von Misescriterion; i.e., yielding occurs when theeffective stress s– exceeds the yield strengthsy obtained by a simple tensile test. Theeffective stress is defined by

where r, t and z denote the radial, tangen-tial and axial directions, respectively.The design axial clamp load for the ring

shown in Figure 3, pg. 4, is Hr = 220,000lbs (980 kN) and results in the followingstresses from equations (2), (3) and (4):

saa = 4850 psi (33.4 MPa)tbb = 5300 psi (36.5 M Pa)sc = 19700 psi (1 36 M Pa)

which are in satisfactory agreement withthe aforementioned stress limits.To cause about 5 percent yielded volumein the ring, the clamping load as deter-mined by the finite element analysis is440,000 lbs (2-0 MN). An effective stresscontour plot of the finite element stresses isshown in Figure 6 , pg. 7, for this clampload; the yielded regions are specificallyidentified (shaded).When the clamp load is increased furtherby 50 percent to 660,000 lbs (2.9 MN)the yielded volume of the ring increases toabout 30 percent. The corresponding effec-tive stress contour plot is shown in Figure 7along with the yielded regions.To determine more exactly the load whereyielding begins (irrespective of stress con-centrations), the 5 percent and 30 percentyielded volume data was linearly extrapo-lated back to zero percent yielding to givea clamp load of 400,000 lbs (1.8 MN)which is a factor of 1.8 or 80 percent high-er than the design axial clamp ring load(Hr = 220,000 lbs or 1.0 MN). This thendefines the maximum (elastic) load carryingcapacity of the central region of the clampring and shows that the conventionaldesign method is adequately conservative.If the clamp load is increased from thedesign load Hr by a factor of 1.8, then the


Figure 5: Bilinear representation of stress-straincurve for elastic-plastic finite elementanalysis.

YIEL

DST

RESS

STRAIN

tan-1 Ep

tan-1 E

54

8

design stresses are increased proportional-ly to:

saa = 8750 psi (60.3 MPa)tbb = 9550 psi (65.8 M Pa)sc = 35500 psi (245 MPa)

Comparing saa to yield strength and tbb(a shear stress) to 0.58 (from equation (5))of yield strength gives no indication thatthe clamp ring has begun to yield, but thefinite element analysis shows that it has.Although the average contact stress, ac, is

somewhat greater than the yield strength(of 30800 psi or 212 MPa) this is of nogreat concern because contact yielding ishighly localized near the contact surfaceand does not present a problem regardingclamp ring failure. This comparison demon-strates that some of the neglected stressesare quite significant, as may have beenexpected, and clearly substantiates theneed for the detailed finite element analy-sis for clamp loads greater than the designload.

Finite element results for the clamp load of660,000 lbs (2.9MN), which is the loadapproximately 50 percent larger than theload to initiate yielding, reveal thatalthough 30 percent of the volume of theclamp ring has yielded, it still retains con-siderable strength and stiffness. Ringdeflections are about twice those obtainedhad the ring remained linear-elastic (for thesame clamp load). For example, at node54 in Figure 4 – the tip of the clamp lip –the axial deflections are 0.0118 inches(288mm) for elastic-plastic behavior and0.0057 inches (140mm) for strictly linear-elastic behavior. These values indicate thatgross deformation is not evident at signifi-cant overloads.The preceding results are to be expectedsince a clamp ring (or any ring) has self-restraint against twisting which inhibits thedeformation that would occur for a straightbeam having the same cross section. Theclamp load on the lip will induce bendingin the body of the clamp resulting in out-ward radial movement of the ends andinward radial movement at the midsection(section a-a in Figure 3). However, thesemovements are partially restrained by thehoop or tangential stresses produced bythe changes in circumferential fiber lengthscorresponding to the radial movements. Astraight beam does not enjoy this kind ofsupport, which is in effect equivalent to theprovision of an elastic foundation for thestraight beam. This overload capacity pro-vides a substantial margin in clamp ringjoint strength to withstand possible over-loads.


Figure 6: Clamp ring effective stress contourswhen 5 percent of the volume hasyielded (Shown shaded).

30.8

2535

30.8

25 20 15 15 2025

10 k

si

Figure 7: Clamp ring effective stress contourswhen 30 percent of the volume hasyielded (Shown shaded).

30.8

30.8

30.8

25

35

35

40

30.8

20 k

si

9

ASME Code EquationThe Summer 1978 Addenda to Section VIII– Division 1 of the ASME Boiler andPressure Vessel Code included new non-mandatory Appendix Z on design rules forclamp connections. Equations for variousclamp and hub stresses are given in theAppendix along with allowable designstresses.Equation 11 in Appendix Z – the equationfor clamp longitudinal or axial stress at theinner radius ri of the clamp body waschecked against the finite element results.This stress is of particular interest becauseit is generally the largest of the clampstresses considered in Appendix Z and isthe sum of the average axial stress on sec-tion a-a and the axial equivalent (linear)bending stress due to the bending momentacting on section a-a. It appears from theform of the equation that it is based on theclamp cross section behaving like that fora straight beam. That is, the equation con-tains no allowance for the self-restrainteffects of a ring-like structure and, there-fore, would be expected to be conserva-tive.A comparison indicates that the AppendixZ value of the average plus linear bendingaxial stress at section a-a is about 33 per-cent larger than the result obtained usingfinite element analysis. For example, at aclamp load of 220,000 lbs (980 kN) thesestresses are:

Appendix Z – equation 11:saa = 32200 psi (222 MPa)

finite element:saa = 24200 psi (167 MPa)

To provide a valid comparison, the finiteelement value was calculated from theforce and bending moment acting at sec-tion a-a. The force was obtained from theintegral through the thickness of a curve fit-ted to the product of the axial finite ele-ment center stresses and the differentialarea. The moment was obtained similarlyexcept the integrand also included the(lever arm) distance from the neutral axisof section a-a.

ConclusionsThe axial design load for clamp rings isdependent on both bolt preload and onloading external to the clamp ring joint.A rationale for conventional clamp ringdesign has been presented employing con-servative stress limits in which basic designdimensions are related to the design loadby primary stress equations easily deriv-able from static equilibrium. Maximumload capacity is determined for clamprings by the finite element method.Elastic-plastic analysis is used to show thatthe clamp ring has substantial overloadcapacity beyond the yield load withoutgross deformation.In a specific example, the equation forclamp body axial stress from Appendix Zto Section VIII of the ASME B&PV Codeindicated a stress 33 percent greater thanthat computed by finite element analysis.

AcknowledgementsThe help of R. J. Gradle, L. A. Gregory,and W. D. Mangieri at RockwellInternational in preparing this paper is sin-cerely appreciated. The author also wishesto thank the ASME and Rockwell reviewersfor thoughtful and constructive comments.

References1. FAI RES, V. M., Design of Machine

Elements, 4th ed., Macmillan, NewYork, 1965, Section 5.9.

2. MEYER, G. and STRELOW, D., “SimpleDiagrams Aid in Analyzing Forces inBolted Joints,”Assembly Engineering,Vol. 15, January 1972, pp. 28-33.

3. Appendices, Section III-Division 1, 1974ASME B&PV Code, Nuclear Power PlantComponents.

4. CLINARD, J. A. and CROWELL, J. S.,ORNL User’s Manual for CREEP-PLASTComputer Program, Oak RidgeNational Laboratory, Oak Ridge,Tennessee, 1973.

5. Guidelines and Procedures for Designof Nuclear System Components atElevated Temperatures, RDT Standard F9-5T, Oak Ridge National Laboratory,Oak Ridge, Tennessee, 1974.

6. HSU, M. B., BERMAN, 1. and PAI, D.H., “An Evaluation of the ComputerProgram CREEP-PLAST” in the ASMEpublication: Pressure Vessels andPiping: Analysis and Computers fromPressure Vessels and Piping Conference,June, 1974.

7. Teledyne Materials Research Seminar onCode Design of Nuclear Components,Vol. 2, pg. 8.3-12,1976.


10

Edward Vogt Valve Company1900 South Saunders StreetRaleigh, North Carolina 27603 USA

Toll-Free Telephone Service(U.S. and Canada)Day: 1-800-225-6989

After Hours Customer Service:1-800-543-3927

US Sales OfficesTel: 919-832-0525FAX: 919-831-3369FAX: 919-831-3376e-mail: [email protected]

Vogt OperationsTel: 812-218-7700FAX: 812-218-7777e-mail: [email protected]

Mexico, Central America & CaribbeanTel: 919-831-3233 FAX: 919-831-3369e-mail: [email protected]

South AmericaTel: 281-564-5671 FAX: 281-564-6052 e-mail: [email protected]

Northern Europe, India & South AfricaTel: 44-1484-602519 FAX: 44-1484-609785e-mail: [email protected]

Southern Europe &French speaking North AfricaTel: 33-4-77-40-18-79 FAX: 33-4-77-89-17-95 email: [email protected]

ChinaTel: 86-10-6505-5548 FAX: 86-10-6505-5547e-mail: [email protected]

Japan, Korea, Middle East & Australasia Tel: 44-1444-443541 FAX: 44-1444-443540 e-mail: [email protected]

Southeast AsiaTel: 65-332-0557 FAX: 65-337-6179 e-mail: [email protected]

Visit Our Website:www.edwardvogt.com


valve clamp stress analysis

Documents