Analysis of Bolting in Flanged Connections (1)
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Analysis of Bolting in Flanged Connections by
Jordan Christopher Baker
A Master’s Engineering Project Submitted to the Graduate
Facuty o! "ensseaer Poytechnic #nstitute
in Partia Fu!iment o! the
"e$uirements !or the degree o!
MAS%E" &F MEC'A(#CA) E(G#(EE"#(G
Appro*ed+
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Ernesto Gutierre-.Mira*ete/ Master’s Engineering Project Ad*iser
"ensseaer Poytechnic #nstitute
'art!ord/ Connecticut
Apri/ 0112
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3 Copyright 0112
by
Jordan Christopher Baker
A "ights "eser*ed
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CONTENTS
)#S% &F %AB)ES444444444444444444444444555 i*
)#S% &F F#G6"ES4444444444444444444444555555555 *
AC7(&8)E9GME(%444444444444444444444455 *i
(&ME(C)A%6"E4444444444444444444444445 *iiABS%"AC%4444444444444444444444444445 :
;5 #(%"&96C%#&(444444444444444444444444 ;05 %'E&"E%#CA) A(A)5 "ES6)%S A(9 9#SC6SS#&(44444444444444444455 ;>
?5 C&(C)6S#&(4444444444444444444444444 02
APPE(9#@ A4444444444444444444444444455 01APPE(9#@ B4455444444444444444444444444 0>
"EFE"E(CES444444444444444444444444445 0=
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LIST OF TABLES
%abe ;+ E!!ecti*e Gasket 8idth444444444444444444455 01
%abe 0+ Gasket Seating4444444444444444444444555 0;%abe >+ Gasket Materia and Contact Facing4444444444444455 00
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LIST OF FIGURES
Figure ;+ #mage o! a Boted Fange Joint44444444444444445 0
Figure 0+ Bot.(ut Connectors Faiures4444444444444444555 >Figure >+ Cross.section o! a Boted Fange Joint44444444444445 ?
Figure ?+ Bot )oad Anaysis44444444444444444444555 Figure + Bot Fiet44444444444444444444444455 ;1Figure =+ Bot %hread44444444444444444444444555 ;;
Figure + FEA Mode o! Bot Fiet4444444444444444445 ;?
Figure + (umber o! Eements *5 Fiet Stress444444444444445 ;
Figure 2+ FEA o! %hread "oot444444444444444444455555 ;=Figure ;1+ (umber o! Eements *5 "oot Stress4444444444444555 ;
Figure ;;+ Fiet Stress Concentration Factor4444444444444455 0>
Figure ;0+ "oot Stress Concentration Factor !or Bending444444444555 0?Figure ;>+ "oot Stress Concentration Factor !or A:ia )oading44444445 0
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ACKNOWLEDGENT
# Doud ike to thank 9r5 Ernesto Gutierre-.Mira*ete !or a o! his support and
guidance5 #t has been di!!icut maintaining my schedue Dith my career/ and spending the
necessary time to compete my Master’s Project to an acceptabe e*e5 # Doud not ha*e
been abe to compete the project Dith out his speedy response to $uestions/ and his
thorough ansDers5
# Doud aso ike to thank Caitin !or her support as De5 She has aDays been there
!or me/ and has aDays been supporti*e e*en i! it meant not being abe to spend time
Dith her5
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NOENCLATURE
Sy!"ol Definition Unit
A b cross.sectiona area o! the bots using the root diameter o! thethread or east diameter to the bottom o! the sots
in0
Am tota re$uired cross.sectiona area o! bots/ taken as the greater o! Am; and Am0
in0
Am;
tota cross.sectiona area o! bots at root o! thread or section o!
east diameter under stress/ re$uired !or the operating conditions
8m;S b
in0
Am0 tota cross.sectiona area o! bots at root o! thread or section o! east diameter under stress/ re$uired or gasket seaing
in0
b E!!ecti*e gasket or joint.contact.sur!ace seating Didth in
b1 Basic gasket seating Didth in9 Major diameter o! bot in
dr "oot diameter o! bot thread in
F p Bot pre.oad b! G 9iameter o! ocation o! gasket oad reaction5 9e!ined as !ooDs+
8hen ≤1b ;? in5 =mmH/ G mean diameter o! gasket
contact !ace5
8hen b05;? GmP
b!
7 b (omina bending stress concentration !actor .
7 d 9irect stress concentration !actor .7 ! Fiet stress concentration !actor .7 t %rans*erse shear stress concentration !actor .
m Gasket !actor .
ne E!!ecti*e number o! oad bearing threads . p Bot thread pitch in
P #nterna design pressure psi
r o
Major radius90
in
r p Pitch radius in
r r
"oot radius
dr 0
in
S Assemby stress psi
Sa AoDabe bot stress at atmospheric temperature psi
S b AoDabe bot stress at design temperature psi8 Fange design bot oad/ !or the operating conditions or gasket
seating/ as may appy5b!
8m; Minimum re$uired bot oad !or the operating conditions5 For !ange pairs used to contain a tubesheet !or a !oating head or a
b!
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6.tube type o! heat e:changers/ or !or any other simiar design/
8m; sha be the arger o! the *aues as indi*iduay cacuated !or
each !ange/ and that *aue sha be used !or both !anges58m0 Minimum re$uired bot oad !or gasket seating5 For !ange pairs
used to contain a tubesheet !or a !oating head or 6.tube type o!
head e:changer/ or !or any other simiar design Dhere the !angesor gaskets are not the same/ 8m0 sha be the arger o! the *aues
cacuated !or each !ange and that *aue sha be used !or both
!anges5
b!
D 8idth used to determine the basic gasket seating Didth b1/ based
upon the contact Didth betDeen the !ange !acing and the gasketin
y Gasket or joint.contact.sur!ace unit seating oad psi
;σ Principe stress ; psi
0σ Principe stress 0 psi
>σ Principe stress > psi
bσ (omina thread bending stress psi
dir σ 9irect stress in root cross.section psi
eqσ %hread root stress psi
f σ Fiet stress psi
iσ #nitia bot stress psi
xσ Pane stress in :.direction psi
z σ Pane stress in -.direction psi
ma:−r τ Ma:imum trans*erse shear stress due to thread bending psi
zxτ Shear stress on pane psi
FEA Finite Eement Anaysis .
C&SM&S FEA so!tDare .A(S# American (ationa Standards #nstitute .
ASME American Society o! Mechanica Engineers .
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ABSTRACT
A mode o! a boted !ange Das created/ using the standards that ha*e been
produced !rom the A(S# American (ationa Standards #nstituteH/ Dhich is pubished by
the ASME American Society o! Mechanica EngineersH and sponsored jointy by the
ASME and the Society o! Automoti*e Engineers I=5
%hese standards de!ine neary e*ery aspect o! the boted !angeK !rom the
dimensions/ toerances/ materias/ and practices used !or manu!acturing the !anges/ as
De as the dimensions/ toerances/ materias and practices !or the bots to be instaed in
the !anges5
%he ASME code has been de*eoped based on a simpe e$uiibrium cacuation o!
an initia bot oad/ a contact pressure o! gasket/ a:ia !orce resuting !rom interna
pressure/ as De as best practices earned o*er time5 %he objecti*e o! this report is to
take the recommendations o! the A(S#ASME !or pre.oading o! the boted !ange/ and
then anay-ing the boting stresses to *aidate their practice5
#n addition/ FEA modes Dere created and e:amined to compare the cassica bot
anaysis theory to Dhat Das determined using !inite eement anaysis5 %he areas that had
been concentrated on Dere the !iet connecting the bot head to the bot shank/ and the
!irst three oad bearing threads o! the bot.nut connection5 Se*era iterations Dere
per!ormed/ each time increasing the mesh o! the !inite eement mode5 As the mesh
increased/ naturay the number o! eements Doud increase/ con*erging the stress gi*en
!rom the FEA mode to the e:act theoretica soution5
%he e:act theoretica soution Das not precisey matched in the area o! the root o!
the oad bearing threads/ due to the imitations o! the so!tDare that Das a*aiabe5
'oDe*er/ se*era supporting re!erences con!irm pastic yieding occurring at the root o!
the !irst oad bearing thread5
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#$ INTRODUCTION
9ue to the recent !ocus on the production o! eectrica poDer Dithout the reease o!
harm!u carbon dio:ide emissions/ emphasis has been paced on the use o! higher
temperature systems !or the production o! energy5 Bot.nut connectors Figure ;H are one
o! the basic types o! !asteners used in machines and structura systems used in high
temperature poDer generation systems5 %hese joints pay an important roe in the sa!ety
and reiabiity o! the systems I;5 #t is knoDn that the beha*ior o! rea a:isymmetric
boted joints in tension is much more compicated than that the con*entiona theory
describes I05 #t is aso knoDn that the oad distribution among the threads in a threaded
connection is not uni!orm5 Most o! the appied oad is carried by the !irst three engaged
threads I>5 A number o! parameters need to be considered Dhen determining the oad
distribution/ Dhich incudes the !orm o! the threads/ the pitch o! the threads/ the number
o! engaged threads/ and the boundary conditions5
Additionay/ Dhen irreguarities such as notches/ hoes/ or groo*es e:ist in the
geometry o! any structura member/ the stress distribution in the neighborhood o! the
irreguarity is atered5 Such irreguarities are caed stress raisers/ and the regions in
Dhich they occur are caed areas o! stress concentration I?5 Lery !eD stress intensity
!actor soutions !or threaded connections ha*e been pubished5 &! these/ most are
di!!icut to use !or comparati*e purposes because o! obscure !eatures o! anayses or
presentation I5 #n most situations/ stress concentrations !actors !or notches e$ui*aent
to a threadH are obtained e:perimentay I=5
%he objecti*es o! this project is to cacuate the bot oads estabished by the ASME
pressure *esse code/ and compute the cassica stress cacuations in the bots to shank
!iet and the oad bearing threads5 A comparison o! the stresses to an FEA mode Di
aso be conducted/ and concusions draDn to support or re!ute the re$uirements
estabished by the ASME code5
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Fig%&e #' I!age of a Bolted Flange (oint
Fange designs Figure ;H ha*e been the subject o! a ot o! criticism !or the past
decade I5 &! major concern is the ack o! the traditiona design procedures I to
$uanti!y the tightness and the e!!ect o! temperature5 8hie history shoDs that most
!anges ha*e been in ser*ice e!!ecti*ey/ probems sti arise5 "ea:ation o! the gasket
due to therma transients and creep are the main cause to bame !or eakage I2/ and a
oss o! more than ha! o! the initia operating gasket oad is commony encountered in
!ange joints Dith certain gaskets operating at reati*ey high temperatures I5 A
comprehensi*e sur*ey I2 conducted in ;2 shoDed that high operationa temperatures
and therma transients are one o! the major sources o! !anged joint !aiure I;15
Ceramic materias are !ar more resistant to the !aiure modes o! high temperaturesthan are metas5 #t may be more practica !rom a materias stand point to choose ceramics
!or the !abrication o! a certain component/ athough it may be more practica to choose
meta !rom a manu!acturing standpoint5 %his decision ogic Di re$uire the use o!
boting to mate the tDo components5 %he boted !ange connections are Didey used in
energy and process pants/ and the design procedure used to produce them is speci!ied in
0
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the American Society o! Mechanica Engineers ASMEH Boier and Pressure Lesse
Code Section L### 9i*ision ; I5 %his design procedure is based on a simpe
e$uiibrium cacuation o! an initia bot oad/ a contact pressure o! gasket and an a:ia
!orce resuting !rom interna pressure I;;5 %he dimensions !or the re$uired boting are
gi*en by the American (ationa Standards #nstitute A(S#H/ Dhie the re$uired materia
and design stress can be !ound in Section ## Part 9 o! the ASME code5
8hen anay-ing a bot preoad/ a *ast range o! actua preoaded *aues that can be
seen by standard tor$uing methods5 %he most common method o! oading a bot is a
tor$ue Drench5 %his method may estabish an actua preoad o! . >1N to the *aue that
Das set on the tor$ue Drench I=5
Fig%&e )' Bolt*N%t Connecto& Fail%&es
&! a !asteners used in structures/ the bot.nut connectors are one o! the most basic
types5 #t has been estimated I;0 that bot nut connector !aiures are distributed as !ooD
Figure 0H I;+
;5 ;N under the head
05 01N at the end o! the thread
>5 =N in the thread at the nut !ace
>
;N
01N
=N
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By using a reduced bot shank/ the situation Dith regard to !atigue !aiures o! the
second type can be impro*ed signi!icanty I;>/ ;?5 Aso/ Dith a reduced shank/ a arger
!iet radius can be pro*ided under the head thereby impro*ing the design Dith regard to
!aiures o! the !irst type I;05 %hese recommendations Dere impemented in the design o!
the bot that Das anay-ed in this study5
%his paper utii-es the anaytica theory estabished by the ASME Code/ Section
L###/ 9i*ision ;/ and Appendi: ##5 %his simper anaysis can be compared to 9i*ision 0
o! the code/ Dhich gi*es the designer greater !reedom o! choice/ but re$uires a detaied
design anaysis to pro*e the sa!ety o! the proposed con!iguration I;5
Fig%&e +' C&oss Section of a Bolted Flange (oint
%he ASME code has standardi-ed a arge *ariety o! !anges/ ranging !rom a O inch
up to a 0? inch pipe !anges5 For the purpose o! this report De Di be e:amining the
boting recommended !or a ;0 inch boted !ange/ as seen in Figure > abo*e5 %his !igure
aso highights the terminoogy used in describing the !ange5 A *ery arge array o!
?
'ub
She
Fange
"ing Gasket
Bot
(ut
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boting materias can be seected based on the operating temperature o! the !ange/ but
since De are interested in energy production appications/ De Di use a high strength
carbon stee boting materia/ SA.?1 B0?/ since higher temperature has itte impact on
its yied strength5
#deay/ a bot Di e:perience ony a ongitudina stress !rom the instaation
preoad5 As stated/ that is idea/ and it shoud be recogni-ed that a prying action can
occur Dith an eccentricay oaded bot/ such as one o! a boted !ange5 #! the sti!!ness o!
a !ange joint is high/ then prying action can be regarded as negigibe I;5 Because o!
the si-e o! our boted !ange connection/ and that the ASME code compensates !or these
stresses/ in the cacuations that !ooDK the prying action Di be negected5
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)$ T,EORETICAL ANAL-SIS
As stated pre*iousy/ the objecti*es o! this project is to cacuate the bot oads
estabished by the ASME pressure *esse code/ and compute the cassica stress
cacuations in the bots to shank !iet and the oad bearing threads5 %he ASME design
procedure is based on a simpe e$uiibrium cacuation o! an initia bot oad/ a contact
pressure o! gasket and an a:ia !orce resuting !rom interna pressure I;;5 A comparison
o! the stresses to an FEA mode Di aso be conducted/ and concusions draDn to
support or re!ute the re$uirements estabished by the ASME code5
8hen designing a boted !ange/ it is necessary to consider the in.ser*ice camping
!orce re$uired !or the assemby5 %he initia camp has to be high enough to compensate
!or a o! the mechanisms Dhich may reduce the camping !orce to the in.ser*ice e*e/
incuding I;+
;5 Embedment rea:ation
05 Eastic interactions
>5 Creep o! meta parts/ gaskets/ etc5
?5 E:terna %ensie )oads
5 'oe inter!erence
=5 "esistance o! joint members to being pued together
5 Pre*aiing tor$ue
5 9i!!erentia therma e:pansion
%he entire sur!ace o! the gasket is assumed to not be competey oaded as a resut o!
!ange rotation5 So an e!!ecti*e areaQ is computed based on an e!!ecti*e DidthQ o! the
gasket5 (aturay/ a great number o! types o! gaskets e:ist/ and the e!!ecti*e gasket
Didth/ b1/ can be cacuated using %abe 0.5; and %abe 0.50 o! 011a Section L### R
9i*ision ; o! the ASME Code5 %hese tabes are repicated in Appendi: A o! this report5
=
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Fig%&e . / Bolt Load Analysis
For the purposes o! this report/ a meta ring gasket Di be anay-ed/ the most
common gasket used in high temperature operations I;;5 Figure ? gi*es a body diagram
representing the inputs !or the bot oad anaysis5 %he e$uation beoD gi*es b1/ the basic
gasket seating width/ as a !unction o! w/ the width of the ring gasket / and is taken !rom
the ASME code5
C1
wb =
;H
Since the basic gasket seating Didth o! our ring gasket Di not e:ceed in/ the
effective width of the gasket / b, as seen in %abe 0 o! this report I;/ Di be e$ua to the
basic gasket seating width5
1bb =
0H
8hen designing a boted !ange connection/ it is necessary to cacuate the bot
oads based o!! o! a number o! re$uirements !or our situation5 #n genera/ the cacuations
shoud be made !or each o! the !ooDing design conditions5 %he !irst condition being the
minimum required bolt load for seating of the gasket W m2H/ and the second being the
minimum required bolt load for the operating conditions W m1H5
'ere/ according to I
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m ! ! W +=; >H
Dhere+
" ! 0ACB51= ?H
"m b ! ;?5>0 ×= H
%he *ariabe ! is the total h#drostatic end force/ Dhereas ! is the total contact surface compression load 5 %he internal design pressure is P/ Dhie G is the diameter at
the location of the gasket load reaction 5 %he term m is a gasket factor / obtained !rom
%abe 0.5; o! 011a Section L### R 9i*ision ; o! the ASME Code/ aong Dith the # term
is the minimum design seating stress5 %hese constants can take *arious *aues/ depending
on the type and materia o! the gasket being used5
b"#W m ;?5>0 = =H
%he total required cross sectional area of bolts $mH and the cross%sectional area of
the bolts $bH using the root diameter/ are cacuated !rom the re$uired bot oads !rom
abo*e/ and the allowable bolt stress at atmospheric temperature SaH/ and the allowable
bolt stress at design temperature S bH5 %he aoDabe bot stress *aues are obtained !rom
Subpart ; Section ## Part 9 o! the ASME code5 %he tota cross sectiona area o! bots Am
re$uired !or both the operating conditions and gasket seating is the greater o! the *aues
!or $m1 and $m2/ Dhere Am; is the total cross sectional area of bolts at the root of the
thread required for the operating conditions/ and Am0 is the total cross%sectional area of
the bolts at the root of the thread required for gasket seating 5 %he bots to be used sha be made such that the actual total cross%sectional area of bolts, $b , Di not be ess than
$m5
b
m
m&
W $ ;
; = H
a
mm
&
W $ 0
0 = H
?
0
r r
d $ π = 2H
r bb $n $ = ;1H
8here d r is the root diameter of the bolts being used in the boted !ange/ $r is the
cross sectional area using the root diameter, and nb is the total number of bolts in the
!ange5 As mentioned earier in this section/ the A(S# codes Di si-e the bots as De as
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the !anges/ Dhich is Dhere De Di !ind our re!erence !or root diameter and tota number
o! bots5
%he flange design bolt load / 8/ is cacuated as !ooDs/ and is then used to cacuate
Dhat Di be used as the indi*idua bolt load / W b5
( )
0
abm & $ $W +
= ;;H
b
bn
W W = ;0H
Section L### o! the ASME code contains a non.mandatory Appendi: S that has
estabished design conditions !or boted !ange connections5 #t recommends that the bots
reai-e a desired stress5 6sing this recommendation/ it is aso possibe to determine the
boting preoad/ ' p/ using the nominal diameter of the bolt / (/ and the e:pected
assembl# stress, & 5
(&
?B111= ;>H
r p $& ' ×= ;?H
&nce De determine the bot preoad/ De Di then anay-e the tDo greatest areas o!
concern/ the stress under the head o! the bot/ and the stress in the root o! the oad
bearing threads5
%he fillet stress/ f σ / underneath the head o! the bot Figure H Di be cacuated
using re!erences to determine the fillet stress concentration factor / ) f / and mutipying it
by the nominal stress in the bolt / iσ 5 Figure ? gi*es the ocation being re!erred to Dhen
considering the !iet stress o! the bot5 %hese are computed !rom the !rom the !ooDing
e$uations/ !i!teen ;H and si:teen ;=H5
A soution using the Finite Eement Anaysis FEAH code C&SM&S Di aso be
de*eoped !or comparison to the cacuated soution5 %he FEA Di be per!ormed using
the eement type and number o! eements that ga*e the most accurate resuts/ comparedto the resuts gi*en !rom the cassica anaysis5
2
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Fig%&e 0 / Bolt Fillet
r
p
i $
' =σ ;H
i f f ) σ σ = ;=H
%he stress in the root o! the oad bearing threads Figure =H can be cacuated by
using the e$uations beoD5 %hese e$uations assume that the -.a:is is in the a:ia
direction o! the bot/ the :.a:is is in the radia direction o! the bot/ and the y.a:is is in
the tangentia direction5
%he root radius r r H/ pitch radius r pH/ and ma*or radius r oH/ Di a ha*e to be
knoDn !or determining these stresses/ as De as the effective number of threads that
carr# the load / ne/ and the thread pitch/ p5
;1
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Fig%&e 1 / Bolt T2&ead
6sing the bot pre.oad recommended !rom the ASME code/ and the thread
dimensions gi*en estabished in the A(S#/ the stresses that Di accumuate in the thread
root can be determined5 %he stresses that Di gather are the direct stress in the root
cross%section dir σ H/ the maximum transverse shear stress due to bending o! the thread
ma:−r τ H/ and the nominal thread bending stress bσ H5
( ) er p
dir nr r
'
00
1 −
=
π
σ ;H
er
p
r pnr
'
π
τ
0
>
ma: =
− ;H
0
;0
pnr
r r '
er
r p p
bπ
σ
−
= ;2H
Furthermore/ since the root o! the threads Di be a stress riser/ a stress concentration
!actor Di ha*e to be appied5 %hese Di be re!erenced ater on in the discussion/ and
incude ) t / ) d / and ) b5
8hen mutipying the indi*idua stress concentration !actors times the
corresponding stress/ the ma:imum pane and shear stresses are determined5
dir d z ) σ σ = 01H
bb x ) σ σ = 0;H
;;
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ma:−= r t zx ) τ τ 00H
%he cacuated stresses can then be used to produce the principa stresses by so*ing
the cubic e$uation5
( )
( ) 10 000
0000>
=−−−+−
−−−+++++−
x# z zx # #z x zx #z x# z # x
zx #z x# x z z # # x z # x
τ σ τ σ τ σ τ τ τ σ σ σ
τ τ τ σ σ σ σ σ σ σ σ σ σ σ σ
0>H
For our particuar states o! stress at our critica point/ this e$uation is reduced to/
( ) 100> =−++− zx x z z x
τ σ σ σ σ σ σ σ 0?H
A!ter so*ing !or the three principa stresses/ the e$ui*aent Lon Mises stress eqσ H
can then be determined5 %his is the e!!ecti*e stress that e:ists at the root o! the oad
bearing threads50
00;
0
; σ σ σ σ σ +−=eq 0H
A soution using the !inite eement anaysis FEAH code C&SM&S Di be used !or
comparison to the abo*e cacuated soutions5 %he sensiti*ity o! the resuts to the number
o! eements Di be in*estigated5
;0
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+$ RESULTS AND DISCUSSION
For the purposes o! this report De Di be e:amining a ;0Q pipe !ange5 %he code
speci!ies that a !ange o! this si-e Di be boted together using a 0Q.?56(C he: head
bot5 %he speci!ications !or these threads can be !ound in a Machinery’s 'andbook I;=5
%he ASMEA(S# code aso go*erns the speci!ication and design o! a boted !ange
under A(S# B;=5 and the ring gasket under ASMEA(S# B;=5015 %he code speci!ies
the dimensions and materia o! the !ange/ as De as the necessary boting and bot
patterns that Di be re$uired !or the cacuations5
A ;0Q pipe !ange as estabished by the A(S# code/ Di ha*e a gasket width o! 5
?>5 %he diameter at the location of the gasket load reaction / "/ is determined !rom
both the A(S# code B;=5 that estabishes the si-ing o! the !ange/ as De as %abe 0.50
%abe ; and %abe 0 o! this reportH o! Section L###.9i*ision ; o! the ASME code5 %he
*aues !or m/ the gasket factor / and y/ the gasket seating load / are determined !rom %abe
0.5; %abe > o! this reportH o! Section L###.9i*ision ; o! the ASME code5 For the
purposes o! this report a *aue o! =5 has been seected !or m, and a *aue o! 0=/111 psi
!or y/ since De Di assume the gasket is made o! either a stainess or nicke based aoy5
%he ma:imum aoDabe tensie stress *aues permitted !or di!!erent materias are
gi*en in Subpart ; o! Section ##/ Part 95 %abe > o! Part 9 co*ers the ma:imum
aoDabe stress *aues !or high aoy stees used !or boting5 %his is Dhat is re!erenced to
determine the allowable bolt stress at atmospheric temperature & aH/ and the allowable
bolt stress at design temperature & bH5
%he total number of bolts n bH used on the !ange/ as De as the thru hoe in the
!ange/ is determined by the si-ing/ gi*en by the A(S# code5 For our ;0Q !ange/ there
are si:teen ;=H bots5 %he root diameter o! these bots is aso estabished by the A(S#
code/ and is gi*en as ;5> inches !or a 0Q.?56(C thread56sing these *aues obtained !rom the ASME and the A(S# code/ and e$uations one
;H through tDe*e ;0H/ the bolt load W H is determined to be ?;/=;> bs5 'oDe*er/ (on.
mandatory Appendi: S o! Section L### R 9i*ision ; o! the ASME code recommends an
assembl# stress/ & / o! the !ange/ that is seen in e$uation ;>5 6sing e$uation ;?/ the bolt
pre%load +' p / is noD determined to be /002 bs5
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Athough this might seem high/ it is important to remember that this is a tDo inch
major diameter bot/ Dhich is much arger than bots used in many major commercia
appications5 Bots are recommended to be tightened to appro:imatey 1 to 21 percent
o! their yied strength I=5 For comparison/ a bot this si-e Doud resut in an
appro:imate preoad o! 00/111 bs !or customary commercia appications5
%he re$uired stress concentration !actors are cacuated !rom Figures ;;/ ;0/ and ;>
I;0/ and are ocated in Appendi: B o! this report5 %hese re!erenced sources ha*e been
determined e:perimentay/ by such means as photo easticity or precision strain gage/
and documented !or design use I?5
A!ter determining the stress concentration !actor/ De can concude that the !iet
stress is /= psi5 A !inite eement mode Das created to estimate the stresses in the
bot !iet and to compare them against the resuts o! the cacuations abo*e5
Fig%&e 3 / FEA odel of Bolt Fillet 4COSOS5
6sing /111 nodes/ the !inite mode Figure H ga*e a !iet stress o! /?; psi/
a di!!erence o! ess than ; N/ Dith respect to the cassica stress cacuations5 #t is Dorth
noting hoDe*er that the number o! eements had to be increased signi!icanty to get these
resuts5 Figure beoD shoDs the resuts o! FEM computations using di!!erent meshes5
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Fig%&e 6 / N%!"e& of Ele!ents 7$ Fillet St&ess
8e Di use the same stress concentration re!erence !or determining the stress in the
root o! the thread5 Another noteDorthy consideration is that not a threads o! the bot
Di carry the oad appied to the bot5 %his stress is not uni!ormy distributed because o!
!actors such as bending o! the threads as cantie*er beams and manu!acturing *ariations
!rom the theoretica geometry I=5
Se*era !actors a!!ect the actua stress concentration !actor !or the root o! a threaded
section5 %hreads that are !ormed by roing betDeen dies that !orce the materia to cod.
!orm into the threaded contour o! the die groo*es are stronger than cut or ground threads
in !atigue and impact because o! cod Dorking/ !a*orabe compressi*eH residua stresses
at the thread roots/ and a more !a*orabe grain structure I=5 Additionay/ the ma:imum
!atigue strength is increased i! the threads are roed subse$uent to heat treatment/ so that
the ensuing Dork hardening and compressi*e residua stresses are not ost5
%he stress concentration !actor ) b/ !or the bending o! the thread/ and as a !unction o!
notch ange is obtained !rom Figure ;05 Stress concentration !actors *ary depending onDhether the eement is in bending or a:ia oading5 %he chart in Figure ;> Di be used to
determine the stress concentration !actors !or 7 d and 7 t/ since these stress are generated
as a resut o! the a:ia oad5
A!ter determining the stress concentration !actors !or the root o! the thread/ De can
then utii-e e$uations 01 through 0 to determine the Lon Mises stress in the root o! the
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!irst oad carrying thread5 %his cacuated stress Das >=/?1 psi5 %his seems remarkaby
high/ and Doud suggest that yieding has occurred in this ocation5 A comparison Das
then run using !inite eement anaysis to con!irm this e:pectation5 Figure 2 shoDs
computed Lon Mises stress o! the thread root using the FEM mode5
Fig%&e 8 / FEA of T2&ead Root 4COSOS5
Per!orming the !inite eement anaysis on the thread root produced a stress o!
;>/;25= psi/ Dhich athough indicated yieding/ Das not in the *icinity o! the
cacuated *aue5 6pon increasing the number o! eements/ the *aue had appeared to
approach the cacuated *aue/ but due to the imitations o! the so!tDare being used/
coud not reai-e enough eements to obtain agreement Dith the *aue obtained/ using the
re!erenced e$uations5 Figure ;1 shoDs a graph indicating the con*ergence o! the
cacuated stress to the FEA determined stress5
;=
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Fig%&e #9 / N%!"e& of Ele!ents 7$ Root St&ess
%he initia specuation coud be that the stresses cacuated !rom the ASME code
e$uations are incorrect5 But upon ooking into the subject/ it is possibe and acceptabe
!or yieding to occur at the thread root5 %he distribution o! the a:ia stress near the ends
o! the oaded portion o! a screD is !ar !rom uni!orm5 %his is not a concern noD because
a:ia stresses are $uite oD/ and because threaded !asteners shoud aDays ha*e enough
ductiity to permit oca yieding at thread roots Dithout damage I=5
#t is generay considered that the !irst three threads Di carry neary the entire bot
oad/ and that the !irst thread Di bear the most oad o! the three5 %Do important !actorscausing this are+
• %he oad is communa among the three threads as redundant oad.carrying
members5 %he shortest path is through the !irst thread I=5
• %he appied oad causes the threaded segment o! the bot to be in tension/
Dhereas the mating portion o! the nut is in compression5 %he resuting
de!ections sighty increase bot pitch and decreases nut pitch5 %his tends to
reie*e the pressure on the second and third threads I=5
%he recommendation using assembl# stress/ (/ is !rom a non.mandatory section o!
the ASME code/ Doud aoD us to use the cacuated bolt load / W b5 %his Doud aoD us
to reduce our bot pre.oad to ?1/;0? bs/ neary cutting our stresses in ha!5 Athough
this might seem ogica/ many other probems arise by not ha*ing a high initia tension5
8ith threaded !asteners/ it is norma !or yieding to crop up at the root o! the bot
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threads5 %he rationae behind this is that the higher the initia tension/ the ess ikey the
joint members Di separate5 Aso/ the higher the initia tension/ the greater the !riction
!orces to resist the reati*e motion in shear I=5
%ests ha*e shoDn that a typica joint oses about percent o! its initia tension Dith
in a !eD minutes/ and that *arious rea:ation e!!ects resut in the oss o! about another
percent Dithin a !eD Deeks I=5 #n some cases/ it is necessary to retighten bots
periodicay during operation5
#t is important to recogni-e that tightening o! bots to !u yied strength shoud not
be speci!ied/ because o! the inaccuracies o! standard bot pre.oading methods/ athough
it is ad*antageous to obtain a high initia bot tension5 #t is signi!icant to be aDare that
the diminuti*e amount o! yieding that occurs Dhen bots are tightened to the !u proo!
oad is not detrimenta to any bot materia o! ade$uate ductiity5 %he ad*antages to
tightening this !orce!uy are+
• %he dynamic oad on the bot is reduced because the e!!ecti*e area o! the
camped members is arger I=5
• %here is a ma:imum protection against o*eroads Dhich cause the joint to
separate I=5
• %here is a ma:imum protection against thread oosening I=5
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.$ CONCLUSION
Mutipe *ariabes are in*o*ed in cacuating the stresses in a boted !ange/ and
rey on a Dide *ariety o! !actors that ha*e an e!!ect on these *ariabes5 %he most
important *ariabes being the thread !orming method a!!ecting the stress concentration/
and the !riction !actor and too accuracy a!!ecting the actua preoad estabished in the
bot5 %his e:pains Dhy the A(S#ASME code is based on a conser*ati*e and simper
anaysis5
E*en though the code Di speci!y a pre.oad/ the *ariation in actuay estabishing
that pre.oad can range !rom . >1N/ and a Dide range o! !actors a!!ect the stress
concentration on the thread root5 Many !actors a!!ect the accuracy o! tor$uing/ but as an
e:ampe/ the !riction coe!!icient is a main dri*er !or the arge *ariation5 But in a
testament to the *ariabe interactions/ Dhen the coe!!icient at the thread inter!ace is
increased/ the stress concentration !actor decreases I;5 %he most accurate Day to
determine the stress concentration !actor is through physica testing/ but e*en Dith this
approach/ the *ariances in manu!acturing can sti produce di!!erent stress
concentrations5
%he !inite eement anaysis Das not e!!ecti*e in repicating the ASME code
computed stress at the thread root5 'oDe*er/ this may be due to imitations o! the
particuar so!tDare *ersion that Das a*aiabe5 %he stress risers in the root o! the thread
Dere so minute that the program coud not generate enough eements to propery reso*e
the particuar area o! stress concentration5 #ncreasing the number o! eements did hep/
but the percent di!!erence/ in computed stress Das sti high in this particuar case5
%he !inite eement anaysis Das e!!ecti*e at repicating the theoretica stress at the
!iet radius !rom bot head to shank transition5 'oDe*er/ due to the si-e o! the bot/ this
!iet radius Das reati*ey arge/ and did not create a highy concentrated stress riser5
Athough the stresses cacuated !rom the cassica e$uations Dere accurate/ the areao! most concern/ the !irst oad bearing thread/ coud not be *aidated Dith the use o! the
!inite eement mode used in the study5 E*en i! this scenario changes/ a arge sa!ety
margin needs to be considered due to the arge array o! *ariabes that e!!ect estabishing
the pre.oad as De as the stress concentration on the thread root5
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A::ENDI; A
Ta"le # / Effecti7e Gas
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Ta"le ) / Gas
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Ta"le + / Gas
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A::ENDI; B
Fig%&e ## / Fillet St&ess Concent&ation Facto& 4Refe&ence #)5
0>
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Fig%&e #) / Root St&ess Concent&ation Facto& fo& Bending 4Refe&ence #)5
0?
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Fig%&e #+ / Root St&ess Concent&ation Facto& fo& A=ial Loading 4Refe&ence #)5
0
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25
I? Srini*asan/ GoDri5 )ehnho!!/ %5F5 Bot 'ead Fiet Stress Concentration Factors in
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0=
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0
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I0= Jaginski/ %5 (imityongsku/ A5 Schmit-/ "5 )akes/ "5 S5 Study o! Bot )oad )oss in
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I0