Analysis of Bolting in Flanged Connections (1)

8/18/2019 Analysis of Bolting in Flanged Connections (1)

1/37

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

i


2/37

3 Copyright 0112

by

Jordan Christopher Baker

A "ights "eser*ed

ii


3/37

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=

iii


4/37

LIST OF TABLES

%abe ;+ E!!ecti*e Gasket 8idth444444444444444444455 01

%abe 0+ Gasket Seating4444444444444444444444555 0;%abe >+ Gasket Materia and Contact Facing4444444444444455 00

i*


5/37

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

*


6/37

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

*i


7/37

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!

*ii


8/37

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 .

*iii


9/37

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

i:


10/37

#$ 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

;


11/37

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


12/37

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


13/37

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


14/37

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


15/37

)$ 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

=


16/37

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


17/37

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


18/37

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


19/37

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


20/37

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

;;


21/37

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


22/37

+$ 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

;>


23/37

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

;?


24/37

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

;


25/37

!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

;=


26/37

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

;


27/37

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

;


28/37

.$ 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

;2


29/37

A::ENDI; A

Ta"le # / Effecti7e Gas


30/37

Ta"le ) / Gas


31/37

Ta"le + / Gas


32/37

A::ENDI; B

Fig%&e ## / Fillet St&ess Concent&ation Facto& 4Refe&ence #)5

0>


33/37

Fig%&e #) / Root St&ess Concent&ation Facto& fo& Bending 4Refe&ence #)5

0?


34/37

Fig%&e #+ / Root St&ess Concent&ation Facto& fo& A=ial Loading 4Refe&ence #)5

0


35/37

REFERENCES

I; Lenkatesan/ Sriman5 7in-e/ Gary )5 "eduction o! Stress Concentration in Bot.(ut

Connectors5 Journa o! Mechanica 9esign/ (o*ember 011=/ Loume ;0/ pp ;>>.

;>?05

I0 Thang/ &u$i5 9iscussion on Beha*ior o! Boted Joints in %ension5 Journa o!

Mechanica 9esign5 May 011/ Loume ;0/ pp5 1=.;15

I> GreDa/ A5S5/ Sabbaghian/ M5 )oad 9istribution BetDeen %hreads in %hreaded

Connections5 Journa o! Pressure Lesse %echnoogy5 February ;22/ Loume ;;2/ pg 2;.

25

I? Srini*asan/ GoDri5 )ehnho!!/ %5F5 Bot 'ead Fiet Stress Concentration Factors in

Cyindrica Pressure Lesses5 Journa o! Pressure Lesse %echnoogy5 August 011;/

Loume ;0>5 pg >; R >5

I 9o*er/ 8595/ Brennan/ F5P5 Stress #ntensity Factors !or %hreaded Connections5

Engineering Fracture Mechanics5 ;22/ Loume 1/ (o5 ?/ pg ?.=5

I= Marshek/ 7urt M5 Fundamentas o! Machine Component 9esign5 %hird Edition5 John

8iey U Sons #nc/ 01115

I Bou-id/ Abde.'akim5 (echache/ Aki5 An Anaytica Soution !or E*auating Gasket

Stress Change in Boted Fange Connections Subjected to 'igh %emperature )oading5

Journa o! Pressure Lesse %echnoogy/ (o*ember 011/ Loume ;0/ pp5 ?;?.?005

I ASME American Society o! Mechanica EngineersH Boier and Pressure Lesse

Code/ 011a/ Section L###/ 9i*ision ;

I2 Payne/ J5 "/ ;2/ PL"C Fanged Joint 6ser’s Sur*ey/ Buetin n5>1=/ 8eding

"esearch Counci5

I;1 Bou-id/ Abde.'akim5 (echache/ Aki5 %hermay #nduced 9e!ections in Boted

Fanged Connections5 Journa o! Pressure Lesse %echnoogy5 (o*ember 0115 Loume

;0/ pp5 >2?.?1;5I;; Sato/ %akuya5 7ado/ 7inchiro5 #neastic Anaysis o! 9issimiar Materia Fanges

Dith Meta "ing Gaskets at Ee*ated %emperatures5 ASME Pressure Lesses and Piping

9i*ision Con!erence5 Juy ;.0;/ 0115 pp5 ;.5

I;0 Pikey/ 85 95/ ;22/ Peterson’s Stress Concentration Factors/ 8iey/ (eD .>5

0=


36/37

I;> Staede/ 85/ ;2>>/ 9auer!estigkeit *on Schrauben/ Mitt5 9er

Materiapru!ungsanstat an der %echnischen 'cohschue 9amstadt/ (o5 ?/ L9#/ Berin5

I;? Liegand/ '5 ;2>>/ 6ber die 9auer!estigkeit *on SchraubenDeksto!!en und

Schrauben*erbindungen/ %hesis/ %echnische 'ochschue 9amstadt/ 9ormstadt/

Germany5

I; Bick!ord/ John '5 An #ntroduction to the 9esign and Beha*ior o! Boted Joints/

%hird Edition5 Marce 9ekker/ #nc5 Copyright 0115

I;= Jones/ Frankin 95 &berg/ Erik5 'orton/ 'obrook )5 "y!!e/ 'enry '5 0th Edition

Machinery’s 'andbook5 #ndustria Press #nc/ 011?5

I; Caister/ 8iiam 95 Jr5 Materias Science and Engineering5 John 8iey U Sons/

#nc5 01115

I; 6gura/ Anse C5 Stresses in Pates and Shes5 McGraD 'i Companies/ #nc5 ;2225

I;2 Beer/ Ferdinand P5 Johnston/ "usse E5 9e8o!/ John %5 Mechanics o! Materias5

McGraD 'i Companies/ #nc5 011;5

I01 Coins/ Jack A5 Mechanica 9esign o! Machine Eements and Machines5 John

8iey U Sons/ #nc5 011>5

I0; Srini*asan/ GoDri5 )ehnho!!/ %erry5 Bot 'ead Stress Concentration Factors in

Cyindrica Pressure Lesses5 Journa o! Pressure Lesse %echnoogy/ August 011;/

Loume ;0>/ #ssue >/ pp5>;.>=5

I00 Barret/ "ichard %5 Stress Concentration Factors !or Fasteners and Fastener Joints5

American Fastener Journa/ JanFeb 0115

I0> @u/ 'ong/ Theng/ Shan.'e/ Maie/ 7ar5 "esearch on the !atigue.creep rupture o!

!astening bots o! utra.supercritica steam turbine cyinder case5 Proceedings o! the

Chinese Society o! Eectrica Engineering5 Lo5 0/ pp =>.==5 ; (o*5 0115

I0? Bou-id/ Abde.'akim5 (echache/ Aki5 %he E!!ect o! Cyinder and 'ub Creep on

the )oad "ea:ation in Boted Fanged Joints5 Journa o! Pressure Lesse %echnoogy5

August 011/ Loume ;>1/ pp5 1>;0;;.; R 1>;0;;.2

I0 (assar/ Sayed A5 Matin/ Payam '5 Camp )oad oss due to Fastener Eongation

Beyond its Eastic )imit5 Journa o! Pressure Lesse %echnoogy5 August 011=/ Loume

;0/ pp5 >2.>5

0


37/37

I0= Jaginski/ %5 (imityongsku/ A5 Schmit-/ "5 )akes/ "5 S5 Study o! Bot )oad )oss in

Boted Auminum Joints5 Journa o! Engineering Materia and %echnoogy5 January

011/ Loume ;02/ pp5 ?.?5

I0

Analysis of Bolting in Flanged Connections (1)

Documents