The Effect of Cylinder and Hub Creep on the Load Relaxation in Bolted Flanged Joints

7/27/2019 The Effect of Cylinder and Hub Creep on the Load Relaxation in Bolted Flanged Joints

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Akli NechachePh.D. Student

e-mail: [email protected]

Abdel-Hakim BouzidProfessore-mail: [email protected]

Ecole de Technologie Superieure,

1100 Notre-Dame Ouest,

Montreal, QC, H3C 1K3, Canada

The Effect of Cylinder and HubCreep on the Load Relaxation inBolted Flanged JointsThe leakage tightness behavior of bolted flange joints is compromised due to the high

temperature effects and, in particular, when creep of the materials of the different com-ponents of the bolted flanged joint takes place. The relaxation of bolted flanged joints isoften estimated from the creep of the gasket and the bolts. The creep behavior of the

flange ring, the hub, and the cylinder is often neglected. Apart from an acknowledgement

of relaxation due to the creep, the designer has no specific tools to accurately assess thiseffect on the bolt load relaxation. The objective of this paper is to present an analytical

approach capable of predicting the bolt load relaxation due to the creep of the flangering, hub, and cylinder. The proposed approach is compared to the 3D finite element

models of different size flanges. An emphasis will be put toward the importance of in-cluding creep of the hub and cylinder in high temperature flange designs.

DOI: 10.1115/1.2937739

Introduction

Bolted flanged joints are widely used as a means of connection

between pressure equipments such as those found in oil refineries,

chemical, and power plants. A major problem encountered with

this type of connection is its inability to remain tight over a long

period of time. The load relaxation in high temperature applica-

tions is the major contributing factor and is due partially to the

creep of the different joint members. Other than an acknowledge-

ment of this effect, the actual ASME Code flange design 1 doesnot give a methodological assessment of the load relaxation and

its impact on the actual joint tightness 2. With the new strictenvironmental protection regulations and the ever-increasing

safety and hazard requirements, some code design procedures

35 are being revised to include this effect. In addition, how-ever, these code designs incorporate the load loss due to the ther-

mal expansion difference of the joint members that is recognizedto cause a major sealing problem in some high temperature appli-

cations 6,7. Other than the mechanical loads, the ASME Codeflange design does not give a specific calculation procedure to

account for the relaxation of the bolt load due to the creep. In

some applications, it was found that creep has induced a loss of

gasket load of more than half of its initial preloading value.

Due to the unavailability of a more complete design procedure,

the designer is often required to make decisions on the basis of

incomplete information and takes a considerable amount of judg-

ment gained from experience and codes of practice. As an aid to

decision making, rational analysis, which attempts to take into

account the most important features of the problem, is an essential

part of the design process.

Although recognized, the long-term creep relaxation in bolted

gasketed joints remains a subject with little research. In the litera-ture, very few papers address analytically the effect of creep to

help engineers estimate accurately the load relaxation in bolted

joints. Creep analyses of bolted flange connections were presented

in Refs. 810. Steady creep was assumed for the flange andbolts. The stiffening effects of the hub and the cylindrical shell

portion together with gasket creep were ignored. The paper pre-

sented in Ref.11extends the analytical approach of Ref.10by

using the strain-hardening rule to estimate the bolt load loss due tothe flange creep. However, the flexibility of the gasket and at-tached structural components of the joint assembly was not takeninto account. Finally, a model based on the elastic interaction ofall joint elements presented in Refs. 12,13 accurately predictsload relaxation due to the gasket creep only. A previous paper14presents an extended work by considering the creep of bolts andflange ring in the axial direction only. The present paper dealswith multiaxial creep behavior of the shell, the hub, and theflange. The analysis of creep is investigated at a uniform tempera-ture. In this study, the effect thermal expansion difference due tothe temperature on the load relaxation is not accounted for sincethis was the subject of previous papers 15,16.

Theoretical Analysis

The current ASME Code flange design rules are based on arigid model and do not account for the flexibility of the differentelements of the joint. Figure 1 shows the proposed model usedthat is based on a previous work 15,16. The flexibility of theflange ring, the cylinder, the hub, the gasket, and the bolts andtheir mechanical interaction is considered. To this model, strain-hardening creep law is applied to the flange ring, the cylinder, andthe hub. The bolt and gasket creep is not considered as this wasthe subject of the previous paper 16. The theoretical calculationprocedure that considers this effect is presented in detail hereafter.

Multiaxial Creep Model. The BaileyNorton equation repre-senting the uniaxial creep law of the steel materials is given by the

following equation:

c =Acmtn 1

where Ac,m,n are the constants that are functions of temperature.

The value ofm is greater than 1; n is usually a fraction. This lawis intended to model only the primary and secondary creeps. Thisequation can be extended to the multiaxial case by introducing theeffective quantities as

ec

=Acemtn 2

where the effective stress is

Contributed by the Pressure Vessel and Piping Division of ASME for publication

in the JOURNAL OFPRESSUREVESSELTECHNOLOGY. Manuscript received April 22, 2006;

final manuscript received January 4, 2007; published online August 7, 2008. Reviewconducted by William Koves. Paper presented at the 2005 ASME Pressure Vessels

and Piping ConferencePVP2005, Denver, CO, July 17-21, 2005.

Journal of Pressure Vessel Technology AUGUST 2008, Vol. 130 / 031211-1Copyright 2008 by ASME

Downloaded 06 Oct 2008 to 129.5.16.227. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm


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e= 12r2 +z2 +zr21/2 3The effective creep strain is

ec

=23rc c2 +c zc2 +zc rc21/2 4

The corresponding strains creep rates are as follows 17:

rc = 3

2SrAc

1/nnem/n1e

cn1/n

c

= 3

2SAc

1/nnem/n1e

cn1/n 5

zc

= rc

+ c= 3

2SzAc

1/nnem/n1e

cn1/n

with

Sr= 1

32rz

S= 1

32rz

Sz= 1

32zr 6

The above creep model is applied to the flange ring, the cylinder,and the hub.

Flange Creep Analysis.For large diameter flanges, ring theoryis applied to the flange annular ring section. The ring is subjectedto the tangential and radial stresses caused by the pressure and therotation of the flange. It should be noted that the axial and shearstresses are neglected.

z=r=rz=z= 0 7

Therefore, for this situation of plane stress,

r=duf

dr=

1

Er+ r

c

=uf

r=

1

Er+

c 8

z=

Er++ z

c

Considering that tangential planes remain plane after deformation,the radial displacement of the flange is given as follows:

uf= ufr+fz 9

where ufris the extensional radial displacement independent ofz

and fis the flange ring rotation. Therefore, the radial and tangen-tial stresses are given by

r=E

1 2duf

dr+

uf

rrc +c

10

=E

1 2uf

r+

duf

drc +rc

The internal bending moment acting the flange ring is given asfollows:

M= B/2A/2

tf/2tf/2

zdzdr 11

Substituting in the Eq. 11 gives

M= B/2

A/2

tf/2

tf/2 E1 2

ufr

+duf

drrc +czdzdr

12

Substituting the radial displacement ufof Eq. 9 and noting thatf is independent ofr and z and ufris independent ofz give

M=Eftf

3lnA/B

121 2

E

1 2

B/2

A/2

tf/2

tf/2

c

+rczdzdr

13

Differentiating M with respect to time t and taking small time

interval Tso that the variation ofMis not significant, the incre-

ment of rotation f can then be obtained:

f=12t

tf3

lnA/B

B/2

A/2

tf/2

tf/2

c

+rczdzdr 14

where c and r

c are given previously by Eq. 5. The creep axialdisplacement of the flange ring at the bolt circle relative to gasketreaction location is therefore obtained:

Fig. 1 Bolted flange model

031211-2 / Vol. 130, AUGUST 2008 Transactions of the ASME



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wfc =CG2 f 15

The radial displacement variation due to creep is analyzed. TakingEq. 8 into consideration:

uf=r

Er+r

c=ufe +r

c 16

Differentiating uf with respect to time t gives

duf

dt=r

c+

r

E r 17

Neglecting the variation of during a small time interval, thecreep radial displacement increment of the flange ring is given asfollows:

uf= rc

t 18

Cylindrical Shell Creep Analysis. The analysis is based onthin-walled cylinders subjected to internal pressure and edge loadsdeveloped at the junction with the hub. Neglecting the radialstress, the stress-strain equations from Ref.18 are used with thecreep components as follows:

z= zexd2u

dz2 =

1

Ez+ z

c 19

=uc

R=

1

Ez+

c 20

where zconsists of two components; a uniform extensional strain

zeand a bending strain. Equations19and20are multiplied bydxand integrated over the shell thickness. The resulting equations

are then multiplied by xdxand integrated over the shell thicknessto give

tc/2

tc/2

zexdx+ tc/2

tc/2 xd2ucdz2

xdx

=1

E

tc

/2

tc/2

zxdx

E

tc

/2

tc/2

xdx+ t

c

/2

tc/2

zcxdx

21

tc/2

tc/2 uc

Rxdx=

1

E

tc/2

tc/2

xdx

E

tc/2

tc/2

zxdx+ tc/2

tc/2

cxdx

Referring to shell theory and expressing the membrane force Nand bending momentMin terms ofand Nzand Mzin terms ofz and noting that Nz =pR /2 gives

Eze=pR

2tc

N

tc+

E

tc

tc/2

tc/2

zcdx 22

and

Euc

R

=N

tc

pR

2tc+

E

tctc/2

tc/2

cdx 23

Equation 23 gives

N=Euc

Rtc+

pR

2E

tc/2

tc/2

c dx 24

Substituting Eq.24 into Eq. 22, the extensional strain ze is

ze=1 2pR

2Ectc

uc

R+

tc

tc/2

tc/2

c

dx+1

tc

tc/2

tc/2

zcdx 25

After simplification of the first equation of the Eq. 21 gives

Etc

3

12

d2uc

dz2 =MzM+Ec

tc/2

tc/2

zcxdx 26

and

M=MzEtc/2

tc/2

cxdx 27

Combining Eqs.21 and2527 and after some mathematical

manipulation, the following differential equation is obtained:

d4uc

dz4 + 44uc=

1

Dc1

2p+ 121 2

Rtc3

tc/2

tc/2

cdx

12

tc3

tc/2

tc/2 d2zc

dz2x dx+

tc/2

tc/2 d2c

dz2x dx

+12

tc4

tc/2

tc/2 tc/2

tc/2 d2zc

dz2xdx+

tc/2

tc/2 d2c

dz2x dxdx

28

where

= 4 31 2R2tc

2 and Dc=

tc3E

121 2

At time t=0, the creep effect does not start, and the creep strainterms vanish so that Eq. 28 becomes the differential equation ofa shell subjected to pressure p and edge loads P 1 and M1:

d4uc

dz4 + 44uc=

1

Dc1

2p 29

The solution of this differential equation has the form of

uc=

2 pR2

2Etc +

ez

23Dc P1cosz+M1cosz sinz

30

Considering the rate of radial displacement and strain at time t

0, the differential equation 28 becomes

d4uc

dz4 + 44uc=

121 2

Rtc3

tc/2

tc/2

c

dx

12

tc3

tc/2

tc/2 d2zc

dz2x dx+

tc/2

tc/2 d2c

dz2x dx

+12

tc4 tc/2tc/2

tc/2tc/2 d2z

c

dz2xdx+

tc/2tc/2 d2

c

dz2x dx

dx

31

Appling the boundary conditions,

d2ucdz2

z=0

= M 1

Dc

12

tc3

tc/2

tc/2

zcxdx+

tc/2

tc/2

cxdx

z=0

+ 12tc

4tc/2

tc/2

zcxdx+

tc/2

tc/2

cxdxdx

z=0

Journal of Pressure Vessel Technology AUGUST 2008, Vol. 130 / 031211-3



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d3ucdz3

z=0

= P1

Dc

12

tc3

tc/2

tc/2 dzc

dzxdx+

tc/2

tc/2 dc

dzxdx

z=0

+12

tc4

tc/2

tc/2 tc/2

tc/2 dzc

dzxdx

+tc/2

tc/2 dc

dzxdxdx

z=0

32

Equation 31 has no known analytical solution and is solved us-

ing finite difference method. However, it is necessary to know thestresses to be able to calculate the strain rates.

Due to the redistribution of load as a result of creep of the shellmaterial, the stress after each time increment is

z=ze+ zt33

=e+ twhere

ze=pR

2tc

Ex

1 2

d2uc

dz2

34

e= pRtc

+ EucR

Ex1 2

d

2

ucdz2

and

z= Ex

1 2

d2uc

dz2

E

1 2z

c+

c

+E

1 2 tctc/2tc/2

c

dx+1

tc

tc/2

tc/2

zcdx

35

=Euc

R

Ex

1 2

d2uc

dz2

E

1 2

c+z

c

+

E

1 22

tc tc/2tc/2

c

dx+

tctc/2tc/2

z

c

dxHub Creep Analysis. Based on the theory developed above,

the differential equation of the radial displacement uh of the hubconsidered as a cylindrical shell with a linear variation of thick-ness through the axial position can be obtained 19:

d2

dz2z2 d2uh

dz2+ 4zuh= 121 2

Eh3

p1 2 36

where

= 121 22ab

2 1/4

The particular solution of this differential equation according to

coordinate z, with its reference taken starting from the point wherethe thickness of the flange is zero, is given as 15

uh=z1/2C1ber+C2bei+C3ker+C4ker

37

where = 2z. Equation 37 represents the radial displacementof the hub at any position. The thickness of the hub at any axial

position is given by th =z, C1, C2, C3, C4 are the integration

constants, which are given from the boundary conditions. berand

bei are, respectively, the real and imaginary derivative parts of

J0ze3i/4, ker and keiare, respectively, the real and imaginary

derivative parts ofK0zei/4.

At time t 0, introducing the effect of creep Eq.36 becomes

d2

dz2z3 d2uh

dz2+ 4zuh= 121

2

ah3

z/2

z/2

cdx

12

3z/2

z/2d2z

c

dz2xdx+

z/2

z/2d2

c

dz2x dx

+

12

4

d2

dz21

zz/2z/2

z/2z/2

zc

xdx

+z/2

z/2

cxdxdx 38

with the boundary conditions given as follows:

d2uhdz2

z=z1,z2

= M 1,2

Dh 12

3z3z/2

z/2

zcxdx+

z/2

z/2

cxdx

z=z1,z2

+ 124z4z/2

z/2

z/2z/2

zcxdx+z/2

z/2

cxdxdxz=z1=z2

39

ddz

z3 d2uhdz2

z=z1,z2

= P1,2

Dh 12

3z3z/2

z/2dz

c

dzxdx+

z/2

z/2d

c

dzxdx

z=z1,z2

+ 124z4

z/2

z/2 z/2

z/2dz

c

dzxdx

+z/2z/2

dc

dz xdxdxz=z1,z2The stresses resulting from the redistribution of load due to thecreep of the hub material after each time increment are given by

z=ze+ zt40

=e+ twhere

ze=pah

2z

Ex

1 2

d2uh

dz2

41

e=pah

z+

Euh

ah

Ex

1 2

d2uh

dz2

and

z= Eh

1 2x

d2uh

dz2 +

E

1 2 zz/2

z/2

cdx

+1

z

z/2

z/2

zcdx E1 2 zc +c




5/9

=Euh

R

Ex

1 2

d2uh

dz2

E

1 2

c+z

c

+E

1 2 2

z

z/2

z/2

cdx+

z

z/2

z/2

zcdx 42

The finite difference method is also used to solve the differentialequations 31 and 38 of the cylinder and hub, respectively. Inorder to achieve a good convergence, it is important to choose theappropriate finite difference time step especially in the stage ofprimary creep because of the high strain rates. The time step is

adjusted according to two conditions. The amount of stress relax-ation cannot be greater than 500 psi and the time step cannot be

greater than 500 h. Typically, a starting time step of 0.01 h is used

and increased gradually until 500 h after only a few hours whensecondary creep is reached.

Compatibility and Elastic Interaction. The radial displace-ment and the rotation due to the creep, calculated at the flange tohub and hub to cylinder junctions, are added to those given by theelastic effect. The total radial displacement and rotation are intro-duced on the flexibility model to determine the redistribution ofthe edge loads at each junction of the hub and the cylinder. Fi-nally, the new bolt load and subsequently the new gasket contactstress are evaluated after each time interval.

Radial Displacements, Rotations, and Edge Loads. The ra-

dial displacement, the rotation, and the edge loads of the indi-vidual bolted joint components of Fig. 1 needs to be considered inthe flexibility analysis in order to determine the bolt load relax-ation. It is to be noted that the creep terms are added for the totaldisplacements and rotations.

The radial displacement and the rotation of the cylindrical shellat the hub junction are

uc=1

23DcP1+

1

22DcM1+

2 R2

2Ectcp+ uc

c 43

c= 1

22DcP1

1

DcM1+ c

c 44

The radial displacement, the rotation, the bending moment, andthe shear force at any axial position are given by the following

equations:

uh=z1/2C1ber+C2bei+C3ker+C4kei

+pah

2

2Ehz2 h+ uh

c 45

h=z3/2C1S1+C2S2+C3S3+C4S4

+2 hpah

2

2Ehz2

+ hc 46

Mh=Eh

3z1/2

481 h2

C1S9+C2S10+C3S11+C4S12

+

2 hpah22

121 h2 47

Ph= Eh

32z1/2

241 h2

C1S5+C2S6+C3S7+C4S8

48

It should be noted that the Bessel functions are detailed in Ref.14. The radial displacement and the rotation of the flange ringare given in terms of the applied loading such that

uf=B

2EP P2

tfK2 + 1

K2 1++ftf

2+ uf

c 49

f=6B

Etf3

lnA/BMf+ f

c 50

Mf is the moment acting on the flange ring and given as follows:

Mf= B

DoM2

Btf

2DoP2+

CG

2DoFb+

GB

16DoG2 +B2p

51

Axial Displacement Compatibility.The system obtained fromconsidering the compatibility of displacement, rotation, and edge

load between the shell, the hub, and the flange ring is staticallyindeterminate. To solve the system, an additional equation thatconsiders the axial displacements is required. This is called therelation of axial compatibility and is obtained by considering theaxial displacement of the nut. It represents the number of turnscarried out by the nut during initial tightening. This displacementremains unchanged during operation and any other working con-dition. It is calculated by the sum of all axial displacements of the

joint individual elements 15,16.

n= wei = wep = wec 52

n=wgi

+wbi

+ 2wfi

=wgc

+wbc

+ 2wfc 53

with

we= FeKe

Fbi

Kb+

Fgi

Kg+ 2CG

2 fi = Fb

c

Kb+

Fgc

Kg+ 2CG

2 fc + fc

54

where Kb is the bolt stiffness and Kg is the gasket stiffness thatdepends on the level of stress reached during bolt-up and is ob-tained by linear interpolation of unloading curves as described inRef. 20. Finally, at each interval of time, a system of 13 equa-tions is formed to solve for the 13 unknowns, namely, C1,C2,C3,

C4, P1, M1, P2, M2, u c, c, u h, f, and Fb 15.

Finite Element Model

To validate the analytical model that estimates the relaxation ofthe bolt load, the result from three-dimensional numerical finiteelement FE modeling of four bolted gasketed joints with differ-ent sizes used in pair were compared. Because of symmetry withrespect to a plane that passes through the gasket midthickness aswell as the geometry and loading, it is possible to model only anangular portion that includes half of the bolt and half of gasketthickness, as shown in Fig. 2. The program developed using AN-

SYS 8.122 was used to treat a 36 in., a 52 in., and a 120 in. heatexchanger welding neck flange and NPS3 slip-on class 150 flange.The geometrical dimensions of the flanges are given in Table 1while the material creep constants are given in Table 2. Thesecreep properties are taken from Refs. 11,21 for which the tem-perature is 1200F in one case and not known in the other case.The material creep properties are beyond the ratings of the flangeexamples and exaggerate the creep effect for the purpose of com-parison between the developed analytical model and the FE re-sults. Other material characteristics used are Youngs modulus of

30 106 psi and Poissons ratio of 0.3 in the elastic range and aresupposed not to vary with temperature for simplicity.

The bolts are made of A-193 B7 material. The loading is ap-plied in three stages. The initial bolt-up is first achieved by apply-ing an axial displacement to the bolt to produce the initial target

bolt stress of 30 ksi to the 36 and 120 in flanges and 40 ksi to the3 and 52 in flanges. The pressure is then applied. The hydrostaticend thrust is simulated by an equivalent longitudinal stress appliedto the shell. Finally, the last stage, which is of the most interest in




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this study, is the application of creep and the relaxation of the boltload over time is evaluated. It is to be noted that for the case of the120 in heat exchanger flange creep was considered with no pres-sure applied. To quantify the effect of creep and the contributionof each element of the bolted joint, the shell, the hub, and theflange ring were subjected to creep individually and simulta-neously together. To emphasize the importance of the creep be-

havior of only the above mentioned elements, the creep of thegasket and bolt were purposely not considered as these were thesubject of previous papers 12,13.

Two types of gaskets were used: corrugated metal sheets

CMSsfor the 52 in. and NPS3 class 150 flanges and compressedasbestos fiber CAF for the 36 in. and 120 in. flanges. The me-chanical behavior of the gasket is represented by nonlinear curvesof gasket contact stress versus axial displacement. These curvesare obtained from load-compression tests conducted on rigid plat-ens. Figure 3 presents the room temperature test data of the twotypes of gasket used in the analysis.

Discussion of the Results

The results obtained from the proposed analytical approach arecompared to those of FE models for the four different flange sizesusing the creep properties of Table 2. Again as stated in the finite

element modelFEM section, the creep properties were selectedto exaggerate creep deflections and compare both the analyticaland FEMs and may not be representative of the actual long-termcreep behavior. Figures 4 and 5 show the distribution of tangentialstress across the flange ring thickness at the flange OD and itsvariation with time when only the flange ring creeps. These graphsindicate that, in general, the analytical and FEA stresses of the

36 in. and 52 in. HE flanges are in good agreement. The higherdifference is observed with the linear stress distributions presentbefore the creep takes place and is due to the flange ring behavingmore like a plate. There is approximately 15% difference betweenan annular plate and a compact ring.

To illustrate the influence of the creep of the hub and shell,Figs. 69 show the bolt stress relaxation caused by the creep ofthe flange ring, the shell, and the hub taken separately as wellcombined for the four flanges. It can be stated that in general theresults between FEM and the proposed analytical model comparewell for the larger diameter flanges. The general trend of loadrelaxation compares well. Table 3 summarizes the results by giv-ing the percentage of load relaxation of the two methods after a

total creep time of 10,000 h. This is just a little bit over a year butis not only enough to illustrate the potential effect of including thecreep of the flange hub and shell in the analysis but also sufficientto validate the analytical model. Up to 50% difference in loadrelaxation is obtained with the NPS 3 class 150 flange. It is ob-served that although the shell creep causes 36% of load drop ascompared to 1450% when the creep of all members takes place,

this represents 1225% of the relaxed load after 10,000 h. 58%

Fig. 2 3D FE model

Table 1 Description of flange geometry

Dimension NPS 3 slip-on36 in.

HE52 in.

HE120 in.

HE

B in. 3.138 35 51 120.25A in. 7.5 48.525 58.375 127tc in. 0.216 1.5625 0.625 0.625th in. 0.216 1.8125 0.823 1.125Hub lenghin. 1 2.491 1.25 3.125tf in. 0.8775 6.625 5.625 2.9375Cin. 6 44.562 56.25 124.5G in. 4.5 36.75 52.625 122.5Bolt nominal diameterin. 0.625 2 1 1No. of bolt 4 28 76 84

Table 2 Creep constants based on NortonBailey law11,21

Flanges Material

Creep constants

Ac m n TF

36 in. HE SS316 1.04 1026 5.35 0.22 1292

52 in. HE SS316 1.04 1026 5.35 0.22 1292

NPS 3 cl 150slip-on

Forgedsteel

9.36 1029 5.5 1

120 in HE Forgedsteel

9.36 1029 5.5 1

Fig. 3 Mechanical behavior of gasket materials




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Fig. 4 Stress relaxation in 52 HE flange

Fig. 5 Stress relaxation in NPS 36 flange

Fig. 6 Bolt stress relaxation in NPS 3 class 150 flange

Fig. 7 Bolt stress relaxation in 36 in HE flange






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of load drop is obtained when only the hub creeps. This represents2633% of the relaxed load. Therefore, the total contribution toload relaxation when considering the shell and hub to creep rep-resents about 3060% of the total combined creep.

In addition, Figs. 10 and 11 show the average axial gasket stressvariation over time caused by the creep effect of the differentelements that compose the flange. Those elements are made tocreep individually or attached to the structure and combined to-

gether to show the influence on the relaxation of the contact stressof the gasket. These results can obviously be used to assess theleakage tightness of the joint assembly. Nevertheless, the resultsobtained from the proposed analytical method are shown to matchreasonably well with those found by finite element analysisFEA. Table 3 summarizes the results of the relaxation of the twomethods after 10,000 h. It is observed that the creep of the huband the cylinder causes 15%, 24%, 30% and 50% relaxations of

the average gasket contact stress, respectively, for the 36 in.,

52 in., 120 in., and NPS 3 class 150 flanges.

It is to be noted that after 10,000 h, 30% difference is found

between the FE model and the proposed analytical theory whenonly the flange ring creep is considered in the case of the NPS 3class 150. This difference is attributed to the fact the ring theorywas used for this case instead of plate theory, which is recom-mended for small diameter flanges. In fact, creep analysis used inconjunction with plate theory should give good results for smalldiameter flanges as well as bolted joints used with blind coverplates that are not treated in this paper.

Finally, this study emphasizes the importance of including thecreep of the hub and the cylinder in the analysis of the bolt loadrelaxation and subsequently the gasket load relaxation in compari-son to the gasket and bolt creep that were investigated in Refs.12,13.

Conclusion

A study on the importance of including the shell and hub in thecreep analysis of bolted joints has been conducted. An analyticalmodel was developed to evaluate the bolt load relaxation overtime. It was found that the shell and hub contribute to up to 60%of the total relaxed load for the examples presented in this paper.Creep of these elements including the flange ring has beencoupled to the axial deflection compatibility equations to deter-mine the resulting gasket and bolt load relaxations. The proposedanalytical approach based on the flexibility of the joint compo-nents has potential for possible incorporation in flange designsonce simplified.

The developed analytical models were compared to the moreaccurate 3D FEA on three different size flanges. The results of theflange ring, the bolt, and gasket stresses and their relaxation overtime compare reasonably well to those of FEA.

Nomenclature cylinder flexural rigidity in.1 strain

strain rate

dimensionless position on hub Poissons ratio hub flexural rigidity in.1 stress of joint element lb / in.2 stress rate shearing stress lb / in.2

t time increment,hf flange rotation rad

Ac, m , n creep constants of joint elements

ah hub mean radius in.A outer diameter of flange in.B inner diameter of flange in.C bolt circle diameterin.

C1 C12 hub constants

D flexural rigiditylb in.Do diameter to flange centroid in.

E Youngs modulus psiKb bolt uniaxial stiffness lb/in.Ke stiffness of joint element

Kg gasket uniaxial stiffnesslb/in.Fb bolt force lb

Table 3 Bolt stress relaxation percent due to creep of boltedflanged joint elements

Percent bolt relaxationdue to creep

NPS 3 inslip-on

36 in.HE

52 in.HE

120 in.HE

Cylinder FEA 5.88 3.70 3.69 4.46Analytical 7.40 2.96 2.43 3.33

Hub FEA 5.70 5.66 8.15Analytical 5.08 4.84 7.62

Ring FEA 47.20 9.20 11.70 23.20Analyt ical 29.80 10.10 12.80 18.98

Ring, cylinder a nd hub FEA 51.60 14.80 20.54 27.80Analyt ical 38.03 14.40 22.03 29.70

Fig. 10 Gasket stress relaxation

Fig. 11 Gasket stress relaxation




9/9

Fe force on joint element

Fg gasket force lbG gasket reaction force diameterin.

M bending moment on shellin. lb/in.Mf flange moment in. lb/in.M1 hub to cylinder discontinuity moment

in. lb/in.M2 flange to hub discontinuity moment in. lb/in.

N membrane force on shelllb/in.P1 hub to cylinder discontinuity force lb/in.P2 flange to hub discontinuity force lb/in.

p internal pressure lb / in.2R shell radius in.

r radial position on flange ring in.S stress deviator, lb / in.2

S1 S12 function depending on ber, ker, bei, kei, ber,

ker, bei, keiT exposure time htf thickness of the flange in.tc thickness of the cylinderin.th thickness of the hub in.u radial displacement of the joint element in.u rate of radial displacement in./hw axial displacement of joint element in.w rate of axial displacement in./hx coordinate through the thickness of shell or

hubin.z axial coordinate in.

Superscript

c refers to creep

f refers to final state

i refers to initial state

Subscript1 refers to cylinder to hub junction2 refers to flange to hub junction

refers to circumferentialb refers to bolt

c refers to creep and cylinder

e refers to effective

f refers to flange

g refers to gasket

r refers to radial

z refers to axial or longitudinal

References1 ASME Boiler and Pressure Vessel Code, 2001, Section VIII, Division 2, Ap-

pendix 2, Rules for Bolted Flange Connections with Ring Type Gaskets.

2 Payne, J. R, 1985, PVRC Flanged Joint Users Survey, Weld. Res. Counc.Bull., 306, pp. 139.

3 EN 1591-1:2001 E, Flanges and their jointsDesign rules for gasketed circu-lar flange connections Part 1: Calculation method.

4 EN 1591-2:2001 E, Flanges and their jointsDesign rules for gasketed circu-lar flange connections Part 2: Gasket parameters.

5 EN 13555 2001, Flanges and their jointsGasket parameters and test proce-dures relevant to the design rules for gasketed circular flange connections.

6 Nechache, A., and Bouzid, A., 2002, The Redistribution of Load in BoltedGasketed Joints Subjected to Steady State Thermal Loading, Proceedings ofthe Tenth International Conference on Nuclear Engineering-ICONE 10, Ar-

lington, VA, ICONE10-22194, pp. 19.

7 Nechache, A., and Bouzid, A., 2003, The Determination of the Load Changesin Bolted Gasketed Joints Subjected to Elevated Temperatures, Proceedings

of the 2003 ASME-PVP Conference, PVP-Vol.457, Analysis of Bolted Joints,

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8 Bailey, R. W, 1933, Flanged Pipe Joints for High Pressure and Tempera-tures, Engineering, 1453771, pp. 674676.

9 Marin, J., 1938, Stresses and Deformations in Pipe Flanges subjected toCreep at High Temperature, J. Franklin Inst., 226, pp. 645657.

10 Waters, E. O, 1938, Analysis of Bolted Joints at High Temperatures, Trans.ASME, 60, pp. 8386.

11 Kraus, H., and Rosenkrans, W., 1984, Creep of Bolted Flanged Connections,Weld. Res. Counc. Bull., 294, pp. 28.

12 Bouzid, A., Chaaban, A., and Bazergui, A., 1995, The Effect of Creep Re-laxation on the Leakage Tightness of Bolted Flanged Joints, ASME J. Pres-sure Vessel Technol., 117, pp. 7178.

13 Bouzid, A., and Chaaban, A., 1997, An accurate Method for Evaluating Re-laxation in Bolted Flanged Connections, ASME J. Pressure Vessel Technol.,

119, pp. 1017.

14 Bouzid, A., and Nechache, A., 2004, Creep Modeling of Bolted FlangeJoints, Proceedings of the 2004 ASME-PVP Conference, PVP-Vol.478, SanDiego, CA, Paper No. PVP2004-2621, pp. 4956.

15 Bouzid, A., and Nechache, A., 2005, Thermally Induced Deflections inBolted Flanged Connections, ASME J. Pressure Vessel Technol., 127, pp.

394401.

16 Bouzid, A., and Nechache, A., 2005, An Analytical Solution for EvaluatingGasket Stress Change in Bolted Flange Connections Subjected to High Tem-

perature Loading, ASME J. Pressure Vessel Technol., 127, pp. 414427.

17 Kraus, H., 1980, Creep Analysis, Wiley, New York.18 Burgreen, D., 1979, Pressure Vessel Analysis, C.P., Jamaica, NY.19 Timoshenko, S. P., 1930, Theory of Plate and Shells, Wiley, New York.20 Bouzid, A., and Champliaud, H., 2004, Contact Stress Evaluation of Non-

Linear Gaskets Using Dual Kriging Interpolation, ASME J. Pressure Vessel

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Documents

The Effect of Cylinder and Hub Creep on the Load Relaxation in Bolted Flanged Joints