Bending iAoments qnd LeokogeAt Flqnged Joints

PART I

ROBERT G. BLICK

, vvrrl.

Dressure on the compression sideof the ''rreutral" axis, and de-creased pressure on the "tension"side of the axis. and that the boltIoad is not affected.

Before using such a simplifying as-sumption, it is lvorthwhile to try tojustify it. It can in part be justifiedby reference to Figure l, rvhich repre-sents a simple kind of bolted assembly.If P is zero, and I, the initial bolttension, is 100 pounds, then G, theinitial gasket compression, must be 100pounds. With P given some value,several types of behavior are possible.

FLANGED JOTNIS dre ol major importoncein the design of petroleum plonts. Yet theproblem ol their behovior under lorces otherthon pressure lodds has received little re-corded thought. If a llange /eoks in service,the gosket is replaced. Or perhops the con-struction crew just heaves up on the wrenchhandle. In extrcme coses the piping may herevised. The problem, once repoired lor aparticular cdse, con ogoin return in onotherplant-generolly is again repoired, andpromptly lorgotten. Unfortunotely it moyperiodically recur os o mdintenonce hedd-ache.

This orticle presents a simple method lorthe onalysis ol llonged joints under a bend-ing-moment load due to weight, expansion,or the like, acting obout the ioint. The con-clusions hove been derived lrom o basis ottheory, becouse ol the obsence of experi-mentol dota. Since every set ol experimentaldota needs some theoreticol bosis-first todetermine what dotd to occumulate, ond sec-ond to make possible on evoluation ol thotddto-the onalysis is presented also withthe thought in mind that some such invesfi-gotion might be stimuloted,

I) If the gasket is relatively inflexible,compared with the flexibility of thebolts and flange, the bolt load will re-main constant2 until P equals the total(initial) bolt load lsince the bolts canapply more load only by stretching,and if they stretch, the flanges sepa-rate. As the {langes tend to separatethe bolts immediately tend to forcethern together again). The gasket loadwill then be zero, and has deereasedat a uniform rate as P lr.as increased.If the load P is further increased, thetotal bolt load rvill increase to equalP, but the gaskets will have lost con-tact rvith the {lange faces. 2) If thebolts and flange are relatively inflex-ible compared to the flexibility of thegasket, the bolt load will increase asthe load P increases. The gasket loadwill remain constant, and in contactwith the flange faces. 3) If the boltsand flange are of about the same orderof flexibility as the gasket, the gasketload rvill decrease and the bolt loadrvill increase, to about the same extent.

Behaviorl is more or less implied instandard flange design methods, asshorvn bv reference to the API-ASI\{Ecode, Section W-317, rvhere 116 (whichamounts to the gasket load) is takenas W-H (.H : total hydraulic end-load,, W - tetal bolt load). It shouldbe noted that despite the fact that thecode goes to great lengths Io auoill.defning tlrc gasket load,. the implica-tion is there. So that, using behaviorlas the most probable, we partly justifythe simplifying assumption that theexternal moment is restrained almostexclusivelv bv a redistribution of thegasket pressuies. British investigationshave also indicated that there is nogreat change in bolt load during ap-plication of hydraulic load. The gas-ket, once yielded, is most likely a rela-tively in{lexible thing, compared tothe axial flexibility of the bolts andthe twisting or rotating {lexibility ofthe flange. Figure 2 shows the gasketacting as a fulcrum, the metallic flangesegment acting as a stiff leter, thebolts represented as a spring, the"trvisting" effect of the flange as athin rod in torsion,3 capable only ofsupplying a nloment load, and the ex-'ternal load represents any kind ofaxial load (hydraulic, axial thrust,etc.) applied to the pair of flanges.Inspection of the figure shows that, ifthe external load equals the bolt load,then the fulcrum load is zero. Sincethe flange can supply only the "twist-ing" resisting momenta necessary tokeep the system in equilibrium, artdno force-loads, it is evident that thegasket load must always equal thealeebraic sum of the bolt load and theexternal load,5

It should be re-emphasized here,that this article is concerned immedi-

BOLIS UNDER TO{ALIilIIIAL TENSIO}T ftr'!I

APPLTED D(TERI{AL LOAD iP"

(r[rriALLY zERo)

Figure I

Simple Bolted Assembly

ent, an 1948rf So-etrole,rry atlarge

\\-nr c h

rr a4cltities..ns toarrel s

rupcd

Nordbar-

:arby-Getr-d ther tirecon-cries, the

co11-

Liorrs

thebeen

.o11S,

Pe-the

:ofkersrde-I-os'eal.

,,lecr

rnIHIS article is concerned directly

with the problem of finding simple cri-teria which will show whether the jointrvill or rvill not leak. The comple-mentary problem of determining thestresses in the flange material (underpressure load) has been well coveredby many investigators, notably Messrs.Waters, Vesstrom, Rossheim and Wil-liams in the United States. Some exten-sion is necessary, however, to includethe effect of bending moment.

If the published gasket coefficientsand constants are aecepted as a pro-visional basis, the analysis is fairlysimple. These various coefficients andconstants are presumably deterrninatefor pressure loads, and have beenestablished with the idea of providinga pressure-tight, or leakproof design.lIf external bendine moments can bebroken dorvn in sote simple mannerthat sholvs ho'rv they affect gasket pres-sures, then these modified gasket pres-sures can be compared rvith the gasketcoefficients, and the pressure-tightnessof the joint including the effect ofbending-moment evaluated along -s1and-ard lines.

Since simplifying assumptions oftenlead to clarification of problems, it isof value to search for some simpli{ica-tion at this point. One possible as-sumplion is the folloning:

That the external moment is re-strained (r'nternally at the iunc-tion of the Ilanee faces) eiclu-sivell by a rediitribution of thegasket pressures. That is. increased

February, 1950-A Gulf Publishing Com,pany Pttblication 101

( SPRING)BOLT LOID

GASKET( FI'LcRUM)

EXTEF.I.{AL

L0ti

I],AN 3E I9I S1!- MOi,fENT("mRsroNu RoD)

ately, not with the flange stresses. butu ith criteria for determinins if tlrejoint rrill or rrill not leak. Alllrouglr.natural l1-. if tlre flanse is rroI strorrqetrorrgh 1o Legin rritlr" tlre joint 1,r.e-sumably rvill leak. Ho.tvever. the ?actthat the fl.ange malr not be orrr.:rslrcs.seddoes not cleterminc that the ioint l'illnot leak. Preserrl flanee slr.esi arralr.ismethods are rcialirelrl lel l-knorrrr indreliable.

Having hypotheticallv establi-qhedthe idea tlrat tlrc exterrril ni()melI i:restrained alrno-st exclusivell- by a re-distribution oi the gasket

-rrressures"

it is necessarr. to dciermine po-.sibleredistribution l)rtlerns. so tlrat sonrekind of boundaries for this "no leak-leak" criterion can be rvorked up.

Since the gasket is not acting in anelastic rarrgc. and for all practical prrr-poses can be considered to change in-sigrrificantlr irr thickness. ser-er.ai Ito.-siL,ilities preserrt llremselres. Figrrie 3shows a cross-section of the saskct"and next to it a ''standard possibiliti"for the lva,v the gasket is loaded, .rvhen

under direct (bolt and pressufe) loadsand berrdinpr loads.

Figure 4 sholr.s a cross-section of

Figure 2.

Flonge SegmentSymbolized

the gasket. and next to it a "maximurnl)ossibilit)." for the r,r.ay the gasket carrbe loaded. under direct and bendineloads. Several other confisurations ar!examined irr llre last sections of tlrisarticle,

Since one of the "best" conditiorrslr'ould be the "maximum possibilitv"case. minirnum requirements can I'edeternined b1- rvorkine rrith that case.

Since manv designeis use the analy.si,s forms in the excellent tleatise"Modern Flange Design" published hvthe Taylor Iiorge Company. the rvriterrrill use the same notation. The nomen-clature cross-references some of theseterms 'r,ith those in the API-ASMEcode.

Using the recommended g-asket con-stanL "m," the minimum total gasketload ean he cxpressed as ''rz''-timcsthe internal pressure times the effec-tive gasket area. Stated matbematicallv.

Hun :2lr:;(irlrlThis establislres the minirnum tolalgasket load not to have leakage.

''l\lodern FIange Design! recom-mends that the unit load on the erossgasket area shou]d nol excecd irrir.t'the sasket yield load.

Tlris establishes the maximum g4s.ket pressure not to have gasket crrish.ing (and, presumably, leakage will beassociated \\'ith any crushing of thsgasket).

Referring to Figure 4, and usinethe above tr.o relationships plus a dglfined quantity "H1;r)' (the yield loadnecessarv to initially seal the gasket)"bv a ferv mathematical operations iican then be determined that:6

I. to avoid gasket crushing (and pre.sumably atterrdant leakagei.

rJ 1+ H",.-H,','l|L\

)

IL to avoid leakage due to in-s1ff1-cient gasket pressure.

Lr . Ho- H,,r.rl'', \ 2

- \l

rr lrclt' H," : ---, atrrl f [ - extcrnal

nr()lnent in inch porrnds.If gasket crushing is discounted as

the factor in lea-kage, then II becomesthe criterion for deterrnining leakage.r. r- H,t -H.lf 11- exceed. "'' 2

''"' tlren the

flange most certainly rr.ill leak. Pro.uided, that the initial a-qsumption. thatthe gasket is relativel,v incompressible,holds true.

['sitrg the H. - H"--I"" criterion

on the example shorvn in "NIodernFlange Design" (a 4t/s-ir'ch thickflange lor 3:l.ineh o.d. pipe. operatirrgat a pressure of 400 psi. and 750o F.):

Hc - f .i1,000Hcr : 107,000

r l\fH- " "' :fl.0tl{J)a

lf _4.1.000 x 3-1

3.1,116: 475,000 inch pounds

If the moment exceeds that r.alue,

Figure 3.

"Stondord Possibility"for Gosket Looding

MOMENT LOADlDot Tm nn

GASKEI THRUFLANGE FAC

GASKET UNDTR IJNIFORMLOAD FROM BOLTING AND

HIDRAIJLIC PRE.SSURE

GASEET UNDER

TARrING LOADFROM IMMElrl

RSSI'LTANTCASTET LOADING

r TENSIONfl

COWRESSION LARGE COI,IPRESSIONCASKET

102 PL:trolcunt, Refner-l7ol. 29, Ittro. 2

rh

1e

rl)

IT

t(

IIi

5qD-rsh-lbethe

;ingde-

oader),sit

'rffi-

pre-

rnal

lasmes*b''

the

Pro-

thatble,

rion

lernhicktingF.) ,

.rncls

Llue,

lity"ing

o.2 February, 1950-A Gulf Publishirry Companv Prftlication

then the joint almost certainl,v rvill

ieak.t This does not mean that a

moment less than 475,000 inch pounds

l ould not cause leakage, since the

natcifiLunl possible value has been de'

termined.

I

I

I

It is interesting to note that- using

half-inch rvall pipe in this case, tlte

pipe stress involved due lo the 475.000-

in"h-pound moment tonlv) would be

about 1200 psi.-rvhich is indeed a

small value, compared with the allol''able stress of 10,400 psi. This shorvs

that there is wisdom in trying to locate

flanges at points of lorv bending mo'

ment-but unfortunately this cannot

ahvays be done.

The writer does not possess eco-

nomic breakdorvn shon'ing the evils offlanged-joint leakage. However, it is

certain that there is appreciable eartr'ings-loss from periodic maintenance

shutdowns. If a reasonably practicalmethod can be'rvorked out to determinethe effects of moment-loads on flangedjoints, therr certainlv tlre small invest-

ment in engineering cost u'ill be rvelljustified. It is surprising that nothinghas been done to establish "momentraiings" for flanges, considering thatcodes specify the pressure-temperatureratings. This is probably because thep r e s s u r e - temperature characteristicsare more obviously related to safet-v,

lvhereas the presence of bending mo-

ment primarily influences the pressure-tightness of the joint. But if flangesleak, an explanation rvhy this happens,and a simple analysis procedure to pre-vent it, is certainly desirable. The fol'lowing sections of this article furtherexpand several ideas in the directionof developing such a procedure.

NOMENCLATURE

Total gasket load required to hold pressure 'i.vithorrt leagageEffective operating u'idth of gaskettrIean gaskct diarneterGasket coefficient-ratio of the requirccl gasket pressure to t

interr-ral hydraulic pressureinternal hydraulic pressrrrc (psi.)

I ""

or Hcp2bGnl

pH, or Hcy Totai gasket load required to initialll' yield (sct) the gasket

l{e Total gasket load\{ Bending moment (inch porrnds)n Total gasket nidthy Gasket constant-"yic1rl" stress (psi.) of the gasket nraterial

Ar or Ar Total bolting area (sq. in.)Sr or S,p Operating bolt stress (psi)

C Diameter of bolt circle1^

-l- Loeflrcrent use(1 to nultipl]' the h1'draulic encl loadK

the charrge in bolt load Iassumecl to decreasc(10) and (11)l

A u (.lrangc i. L,,,lr lerrstl, ! Tr.ni.^l

Ar" Changc in bolt folcc | ' ^

A.r Change in rnornelltEn E,lastic constant of half the bolt t""ett;-4(.,ier"u

X,,p,,

-C;rip

Lctrtfth 72 -Iralf the ga-sket thickr't.ss: #/" =

_.-Gasket Contact Are:r X "li"Ciasket Thickness /2

El:rstic constant of the flange: "f /Radian :Total Bolt Load X I-ever Arttr

R"s,tltittg A"grtiir Rot"ti* G Rt,li,,tt

to obtain

folmulas

NO'f!lst llcduce.l to essenlials, the I)ressure oll the

gasket coltiiitt surflces should not be iessthan "rD" ljnes the internal pressure' nor beso g:reat ttrat an "uliirnate compression allow-abtc' (that clcllerlds or1 tlle gAsliet ]'ieldlroint) is er|eedcii. 'I'hese constalrts a.e Eien-erally found in the API--ASN{E co.le, Se(ltion\\.-31?. 1'het are Dot rnancliltory.

2 c)r in fact lrral_ de(rrease sonrelthat.3 Although, of ( ourso, the flange is nor

under "torsi!rn" i1s such.{ Tending to turrl it inside-out.5 If the bolt load is assumed to decrease

with application of external load, the gasketload must allYays equal ress th&n the algebraicsum of the 1:7?r:Iiol bott load and the ext€'rnalload. By proceeclilrg on the assumption of acorlstant bolt load. results nlay be obtaiDed

rvhich &rc less obscure, aDd whi.rh do rlotprevent subsequenL corrcctions for changingholt-load- Il can be reaclily seen, for iilstance,that if tlre flange is extrernely flexible rota-tionally, il Nill behave cxactl},- likc & le!er,ln that casc, the bott load reduction lvoulddepend on the reletive distance of the externaltoad to the fulcruD and the bolt loa.c1 to thefulcau rn.

6 Assuming the siml)lest typc of gasket.? "Lealiage" is a vague term. -{lrnost all

joints continuously leak to some small extent.It would l)e more correct to say that, "thejoint is definitelt' operating: outside therecommendeal linril.s Ior reasonable assuranceof n.glicil'lp l'.Nkrg..

End. ot' Part I. Part II uill appearin an early issue.

Figure 4.

"Moximum Possi-bility" for Gosket

Looding

MO},TENT LOA!APFLIED TO

GASKETFtA\GE FACES

COMPRESSION

GASKET IJNDER INIMRMLOAD FROM BOLTING AND

HYDRAIJLIC PRESSIJRE

GASKET IJNDE1TVARYINGtr LOAD

FROht M0MENT +

RESIJLTAilTG.{SKET LOADING

LARCE CCI.PRESSION

Ies

Jto

rh,roles

est

le.

T_lIJf tnSf the basic assumption is made

that the bending moment t'ill be re'strained exclusively by a redistribu-tion of the gasket loads'

The unitl gasket load necessary tohold the pressure without leakage:

fc*r": *mp (1)

The unit gasket load not to be ex-

ceeded rvithout danger of crushing thegasket:2

- ),,-

eJ

Hou'ever, this is the maximum valuecomputed over tlre gross gasket area,

ruheiea. the effeetivi operating gasket

rvidth is 2b. The apparent erushingstress allowable on the basis of a

rvidth of 2b is:

n l'n /)\tc^"": rl.2h. : . b.

\.1

The unit gasket load due to the

bolting:Bolt Load

rub - | Effective opcrating gasket area

- | AoS"n- --zwc-The unit gasket load due to hydrau'

lic end load: \. HYdraulic End Loadrcn:-r"r'

Effective operating gasket al'ea

__,ir/4Grp ___9p2birc 8b

May, 1950-A Gulf Publi'shing

The "extreme fiber" unit gasket loaddue to a bending moment:

: (t) fau (3)

Total unit gasket load:fc : fcs * fco -F fe.t

- An S,o

- -QP- * f,r,,zb,iic 8b

From formula ( 1) :

la 2 fc",t"fcB*{co-fc.t ) fc"""

-fc.r ) fc-,"-fc"-fcoferr ( fct*fco-fc''t'

ICritcriorr for srrfficielrt gasket Pressurel(4)

lN PARI I several ideas ol qauolitotive nqture were dis-cussed, towqrd the develoPmentof o simple method to deline themoment caPocitY ol llongedioints. Part ll Presents o mothe-'moticol

oPProoch deriving some

of those relotionshiPs necessoryto more accuratelY deline thiscopocity. Introduced is s "leok-oge enieloPe," o groPh on whichthe operating moment-Pressurecondiiions may be Plotted, com'pored with the coPobilities ofthe ioint, ond the morgin agoinstleokoge reodily determined.

From formula (2):fo < fc-"-

for*f"offaor ( fe-"'fcu ( fc-""-fc"-f6,

ICriterion for excessive gasket pressure](s)

It is now necessary to determine f611.

This may be done rr.ith the followingassumptions:

(a) That each circle defined by thegasket surfaces remains planeat the flange faces.

(b) That the unit load distributionon the gasket due to bendingmoment has the customary'otri.angular" pattern, increasinguniformly from the centroidalaxis, or:

(b)'That the unit gasket load dis-triliution due to bending mo-ment has some other pattern.

Assuming (a) and (b),r-rc\I -

MSection modulus of gasket

- I\{

n/4 G'2b

Then formula (4) becomes:II 1 Ae S"o Gp

;/icr:r \ 2bnc - 8b -"'uor. "o;t""-'f(++b-)

(6)

And formula (5) becomes:II ln AB S"" , Gp

7+c'5o rr - Zbnc - sb

r\f <n_itG' r rG')'rL_ G_aq!er--r-24(7)

On the other hand, assuming (a)and (b)', one may refer to figure 5,rvhich shon's the gasket under somesymmetrical (but random) stress pat-tern due to bending moment. Workingwith this figure, equilibrium requiresthat:

v =zJG/z f*ry y dao

Let f", : some mean value of fcot",such that

xt - zt,, (G/2 1' rlaJa,

b,,, fG'2 :''1^.= Q - Statical ntomentoI €{asKet

trI :2f* Q :2f- bG't,ft-rm

- -4,.-lD Lr'

Lct the maxirnum perrnissible rralue forf- be

f", : fart

henthel1€-ch-ardtheac-r ri-ses

ctsof,'

rtoiie-

es-itu)erlerto

ni-

PAR.T II

ROBERT G. BLICKBox 232, Sun VolleY, Colif.

hengn-

ry,ndntid.

rl.:(l

)nS-<e

lciha

le

trTENSION|r

COIIPRESSIONGASKET

Figure 5. Gosket Under Rondom Stress Due to Moment'

Bending Xloments ond Leokoge

At Flonged Joints

C orn,pany P u'blicttion

t-IG\I - 2b G"

t 19

N{ / AB S""2b G" - 2bqr G

MzYnzbc"\b-

u<o 9'4

Then formula (4) becomes: {- _ Hydraulic end loarl- Bolting Area

: -;r/4 Gz pA

The bolt stress due to the minimumgasket load requiremenr (to holdpressure):

,- _ Area of gasket times (nr p)rBsISolring Area

Z qzb:lpAr

The "extreme fiber" bolt stress dueto bending moment:

_t

Assumine that the bolt stress due tomoment is "trianeularly" distributed:

l_rB\I -

tr{omentSectiorr n)o(kllus of l,6l1i11g nr"^

The total bolt ,.tress must not exceedSno. the allorvable bolt stress. II

S.o > fr,,*f"**fnn,c : f,G'I

' 2rtil'rrrp , +II-1.4,' Ao C-{"

trl <CA"S, - 1,icc/t: \+ j't'' -1"'''

_ Fi-gure 7 defines the "leakage enve-lopeo' under this assumption. It u,ouldbe more correct to call this envelopean "allo.rvable liolt stress envelope,"since, l'ith this type of behavior, theflange rvould not' ieak until the boltsfailed. The .rvriter n'ould speculatethat, if joints leaked onlv l'hen boltsfailt'd. tlrele slrouirl irr,leed he

"leakage envelopes" may be dralvn foranv fl ange, bolt, and gasket cornbination.Figure 8 has been made for an B-inch-150-pound raised face carbon steelflange_ rvith a compressed asbestos gas-ye.t 8l/z inches i.d. by tl inch rvide.The bolts are assumed to he A-96.Grade A. The florv temperature is takenas 5000 F., and the bolt temDeratureis assumed to be 4500 F. (90 per centof flo'n temperature) . Under these cir.cumstances. the flange is operating atits-primlry service pr".rut" rating of150 psi. Norv. assumi'ng thnt tlte llanseu,ould not /ail, inasmuih as rhe'speii-fied bolts have an allorrable streis of16,250 psi., at a "factor of safety', ofl. the follorring data can lre sei up:

BoltsI at t7t,, clta.S,,r : 16,2-50 psi.

Go-

F-rilP6D

11 q -G4i!es -o(-G"ti -\ 4

And formula (5)

lor0oor0@

81000,000

6rooorooo

4,ooo r0oo

2,0oo,0o0

becomes:

An S,,o ' Grr2a.c - -8b

f2G'yn--941 S'" (s)

f (IICf,.POIII{DS)

Referring to formula (6) :

" " oiS:, -r,'.":( 3 .b,,)

rr.9\1.+lYt6,2-r0l}r \

trI ( 8it,J00-222p

\\-hcn p : O, fI < 88,300 inch pouncls

\\'l,crrlr -{).p: -i:TO -JOSpsi.

. A straight line is drau'n intersectingthese poinls, forrning part of the leaklage envelope.

Referring to for-mula (7) :

3.1.116 x f. i-fl()

lerv ferv cases of joint leak-age.

-{s arr example of horr these

*2bG'm)(8)

. Relationships (8) and (9) expressIhe maximum possible moments con-ceivable3 (under the basic assumntion)without leakage. Thev correspond toth_e "maximr- pos.ibility" ease ofFieure 4.

Again using the example in ,,N[od-

ern Flange Design." the "leakage en.velopeso of Figure (r have been d-rarvn.shorving maximum bending momentversus pressure. The ordinaies for the"rectangular" distribut iot-t are 4/rtimes the ordinates for trianeular dis-tribution.

It is of interest. at this point. tocompare another assumption. otherthan that the moment is'resisted ex-clusively by a redistribution of gasketpressures._Assuming that the unil gas-ket load does not chunge rvith ap'pli-cation of bending moment, the 6oltsmust resist the nroment. This is the(improbable) "Behavior No. 2,' men-tioned earlier.

Another "leakage envelope" may beconslnrcted on this hasis.

The bolt stress due to hvdraulicend load:

l\I , r. 1. , .. i, r. .\,, 2.JJ sq. in(..\r,. .: , a -

(ttalileter ol IrnJl 61r.1a;

GasketG:9"b: tA"

rr-/(nn

-+

-e 3'1-11rt

"( : + I,x2.s)

rt(p

t

t 14lq X j X {0t\ 2,, 2 \l !? x2q

i,i

t6140_

II < 143 p + 287,000-88,300

\t<143pf198,700at p -: O, \I : 199,769 it.r."

lrour rls

at p : 100, }I :213,669 1tr.',porrn ds

A straight line is drarvn inter-,secting these points. Since it doesnot inter-sect the first line. it iscr ident tlral "crushirrg" the gas-ket is not a factor in this case.This rvould shorr that a better

Figure 6

P robo bleLeokoge

E nve lo pes

p( prr)

t20 Pctroleunt Reftner-l/ol. 29, Ilro. 5

sket- 9t'= %,,=2 \.4500

;\-+Dnr I\)l

dralvn formbination,an B-inch-rbon steelbestos gas-inch wide.be A.96,

rre is taken)mperature0 per cent: these cir-rerating atI rating ofthe t'langethe speci-

e stress ofsafety" of)e set up:

f-xzs)

ch pounds

: 398 psi.

tersectingthe leak-

x]!]soI

BB,3OO

inch

) inch

wn inter-ce it doesine, it isthe gas-

.his case.a better

No. 5 May, 1950-A Gulf Publishing Company Publtcation

(plt)

l2L

10,ooo,ooolrgure /

lmproboble"Leokoge"

Envelo pe

8,00o 1000

6rooo rooo

/+ 1000 r0O0

2,0o0,0o0

choice of gasket materialt could havebeen made. A gasket rvith a lorver ygenerallv has a loner m, and conse-quently uould be more efficient. Itwould raise the rieht-hand end of thefirst line [from foimula (6)], allow-ing greater moments at higher pres-sures.

Getting Lack to the primary pres-sure rating of the flange, a heavy linehas been drarvn vertically from I50pounds on Figure 8. Study- of the mo-ment defined bv its intersection \\'ith

the leakage envelope leads to the fol-lolvine conclusion:

Thal lf the flanse will not be over-stressed rvith 4-96. Grade A bolts,then it rvill probably not be over-stressed at 150 psi. with a bend'ingmoment ol 55,000 inch pounds simul'taneously applied.o Some readers maycare to run a check on this flange forthese operating conditions. rvith thespecified bolting. It should be notedrhar some of thJ B l6E flanges do nothold up under a standard pressure

analysist-but rvork satisfactorily de'

spite this mathematical obstacle.Fieure t has been constructed for

this same example on a quite different,conservative, basis. Starting with theconservative assumption that theflange-gasket-bolt combination can (at150 psi.) carry no bending momentrvithout danger of leakage or dangerof flange failure, the following canbe deduced:

Referring to formula (6) :

\r<co;t''-o'?"(f+r*1

.P(psl)

I (r!{cH-P0urDs)

-l--200 ro0o198,

1@,ooo

120 r0oo

NA--t80,0o0

40,ooo

Figure 8

Leokoge Envelopefor 8-lnch,

1SO-Poun{ Flonge

p

,ftlrl

Total gasket load required to ho1c1 pressllre n,ithorrt leagageEffective operating $,idth of gaskettrfean gasket dianreterGasket coefficient-ratio of the requiretl gasket pressure to theinternal hydraulic pressureintcrnal hydraulic pressrrre (psi.)Total gasket load reclrrirc<l to initiallr- 1..ielcl (set) thc gasketTotal gasket loadBending moment (inch pounds)Total gasket s,idthGasket constant-"yielcl" stress (psi.) of the gaskct n.raterialTotal bolting area (sq. in.,Operating bolt stress (psi)Dianreter of bolt circle

There are several factors that influ.ence th_e_ leakage envelopes of flangedjoints. Chief among these is the chaigein bolt-load that occurs rvhen intern"alpressure aud bending momenl are ap-plied. In Part III some of these fai.tors are evaluated. and an analyticalmetlrod is developed to drarv envelopesthat include the effect ol the dlnami-callv changing bolt-load.

. End ot' Part II. Part III will appeartn on earLy t,ssue,

\OTESrlt is $ortlri" 0f note that ISritish investi-gations tend to indicate that the ratio of the(total ) h]-draulic load t.o the net (total)

g:rsltet load is deterntinate, rather thaln the|atio of the htdraulic l)fessure to a unitBask.it load. This $-oulcl tend to require agasliet load per inch of circunference (notr.lated to gasl<et \ridilr) dependent on{llalrleter, }rressule an(l a q:1sket constant.:l'he unit gasket loa{1 trot to be ex{.eeded\\-ithout danraBing thc fl.rtrge contact fa(.e-s isnot (.onsidcfed here.

3 (larcful retiglrterriDg oi the bolts after:rpplicatioD of pressure Dlight in effe.t pro-,lu, o llri{ ,listril,uri^rr l,iltprn, if it \routdllot occur normall]-.

{ These tnight ilot. (orre.tly be called"leak&ge en\-elopes lrith fixed bolt load_,,since the installeal bolt load rvill determiiethe gasket lo.d. -{s arl example of what thisrneans, the bolt load has been taken as Asrct(41.6 sq. in.) times ttle allo\yatlle ol)eratingirolt stress of 13,11)r) l)si. If the bott load hadL,ppn takpn as (ABAc, I, .{n-inr : 2, a smaller!alue. thF Frrt ploppj s orrl,l L,p smallpr, The"crushin8" part of thc envelope would moveup, but the "insufficient g.ashet pressure,'parts-oul(l nloye to the left. If the bolt areaand/or bolt stfess lrcre increased, the"crushing" part of the envelope would movedos'n, but the "insufficient gasket pressure"part \rould move to ilre .ignr,

5 Or perhaps a smaller width.-

6 Due to the relatively sman effect on theilango-monrpltls oi shifring 1,art of tlrp Hcluad to HD, and vi.e r "rsa. This will inl rorlucian effective "torsion' on the cross-section ofthe flange, lvhich.ran lrobablt be ignored,r lrua lo hA rilrq I,epn ill .ommon u."e betorethe de|elopnent of ilre present method offlange stress anal)-sis. 1.his particular caseshoulcl proye satisfactory.8An "effcctive bolting,', so to speak.

300

NOMENCLATURE I

Hn or

p

H" or lf6,

rf^2bGIN

L,Ising the same gasket as in the pre_ceolng example,

trI < o (Ao S"o) -

))) n'A

at p : 150 psi ( rlre primarl. servicepressure rating)

o< 9A

(AR S.,,) - 222 x 150

'1A" S^,) - -222 X 159 - ra xrroz.zl

servative leakage envelope of Figure 9is drarvn for this joint. That this is aconservative envelope maY l)e demon-.strated as follorvs:

Ar S,,', : l4,ggg

Ilnt Ar :2.42 sq. in.

e _ 14,800

""': -'2llL' : 61oo Psi'

In other lvords. on this basis eventhe use of Grade A-107 carbon steelbolts, rvith an Sop allowable of 6875psi. rvould be excessive for theseflanges. In fact, these bolts r-ould noteven,develop the load necessar)' toinitialll'_yield the gasker for propersetting. Figure 8 is probably the mbrecorre_ct envelope for this joint (pro-vided 4-96-4 holts are used).

Using thisa maximump: o,

value of (AB S,,") to obtainpermissible moment at

II< ftla.s00;- 222X04

tr{ :33,200 inch pounds

By dran'ing a line intersecting thispoint and M: O at 150 psi." the con-

Figure 9

Conse rvotiveLeokogeEnvelope

200,000

160,0o0

120,000

40,000

t

r

I33'

Pctrolettm I?efiner-\,'ol. 29, No. 5

Bending lAoments qnd Leokoge

At Flqnged Joints

PAR.T III

ROBERT G. BLICK

Box 232, Sun VolleY, Colif

Figure 10. Lood-Deflection Curve for Compressed Asbestor

nlication of Pressure lo some final

i'alue. and tlren reduction of pressure

[o zero.The return-path has a greater sloPe

than the increase'path-that is' the-gas-

["i-i. 4tln*" unier a decreasing lo-ad

tt un una.t an increasing load' Tlris

can be deduced from purely theorellcal

considerations. Assuming that the,gas-

ket rvill take a permanent set' ther-e

*lif U" a positive amount of rvork

Jrt* i" tlre total compression cycle'

The shaded area in the figure repre-

sents the net loss of enerqv for a com-

lN PARI It ol this series, mothe-moticol relotionshiPs lor ioint-tiofitness were derived that os-

tii" o constont boltJood' Also,the ideo ol q "leokoge enve-

lopel' plotting Performonce ca-

oitititi"t ol the- ioint, wos deter-'i,in"a. This concluding orticlediscusses seYerol other lactorsand derives the mathemoticsnecessorv to evoluate the effectol the dynamicollY chongingbolt-load.

Dlete cvcle.l That there must be a net

io.. foi an\ Portion of the cvcle can

also he deduced - for otherrvise itrvould be possible to oPerate over a

Dortion of-the cycle and obtain per-

netnal motion.' Since gaskets lre stiffer utrder re-

au"i"g lou,l. th"t" will be a shift of*r"::"?"".f ;' axis torvard the "tension".iJ" of the centroid. Figure^ lI shorvs

an exaggerated piclure of tllts he-

havior. ictuallr-. the shif t of tlre "neu'

irut;; u*i. l'ill'probablv be extremely

sl iglrt- so tlrat calcrrlations ma) lre

-Ja" o" tlre assrrrnption that it coirr'

cides rvith the centroidal axis'Sonre invcstigators 1nay care to run

load-deflection tesls olr Practrccl gasKet

material . The load catt hrst lle run-up

to..ih" ittltiul bolt-load value, and then

r"a*"a to the operating vah'e (that

oh,"in. rrhen llre joirrt is under lres'sure). Then the load can lre reduced

to the valrre corresporrdin s to . ( n:p ).

irt otte lest- arld inercascd an equllalenramount (or to a load corresPondlng

io tlt. gu.k"t ''cruslritrg" load) in an'

other test. These tests clll l)e rePeatecl

for a number of cvcles' From the re'

."i,i"* "tit"s the relative stiffness -of

if'"' *l.f."t urtcler increasing and de'.r"u.ing loads mav Ite determined' l he

.l'r;t, oi the neutral axis can be com'

puted from this data'

Similar load-deflection tests mal- be

t""i" f.t the {lange and bolt combina-

iion toithout a gasket' or the flange ro-

tations arrd bolt deflections may he

computed. The lesulting curves may

be compared uith tlre gasket curves'

In this rval'. it can readrt)' tt9. o9'

termined rvhether tlre gaskel really rs

appreciablv stiffer than the bolt ano

nii'-.t .";Uination. and rthether the'U"ti?-.i-piiiving

asiumption is a validone.

Corrections for Change inBolt-Load

The logical starting point. for cor-

rer:tion ol tlre leakage envelopes I or

change in bolt'load is to determine-tl'r"tii"t the bolt'load decreases or in'..""."" after ltressure is appli.ed' Con'

clusions ma1 tlren be reaclred regard'

ii

B1

Ei

f

TTU P fO this point. it lras heen as'

.ilred that the t'neutral'' axis of the

n".1", ..i""ides rvith the centroidal

l*L. ftti. is ttot necessarily so' Horr-

ever. it is a logical assumption" an!

Probablv a correct one for all Practr-cal purposes.

Figuie l0 is a qtralitative represel-

tatioi of the stress-strain characteris-ii.. of compressed aslreslos' lt shou s

-thut ttupp.ns rvhen a load is graduallyanplied't'o and released from the gas'

i[i- R.tott. on the curve indicate the

Jir""tio., of the cvcle, from initial ap'1S

rdn-

ry

,.'s

'&1i*tfr,E

Iunc, 1950-4 Gulf Publishirtg Contlany Publicationt29

r+_ SMATL COMPRESSIOH

I

COMPRESSION

Figure ll. Shift of"Neutrol" Axis

I

l

_LSIITT--T-i:

I

CHANOED GASKET LOADDI'E K} iOMENT

TAL COMPRESSIOIf

INGE COMPRESSION

ing its behavior when moment is ap-plLd. If the bolt-load d,eueases,'itmeans that the joint will start to leak,and the gasket to crush, sooner (at asmaller moment). The converse willbe true if there is an increase in bolt-load.'z The simplest, and probably aneffective, correction may be made byaltering the value of As So, in thecriteria formulas.

Actually, A" Son will be a functionof the pressure and of the moment,rather than a constant. To illustratethis further, assume that the bolt-loadwill decrease as internal pressure isapplied. Then the value of As S", willdecrease as pressure is applied. Themaximum pressure capacity of thejoint with no moment will be smallerthan figures based on the initial bolt-load would imply. Assuming the jointto be under some intermediate pres.sure, and moment to be applied, themaximum value of the allowable mo-ment would be smaller than formulasbased on the initial bolt-load, or forbolt-load corrected for pressure only,would imply. This would be so fortwo reasons, On the "tensiontt side ofthe neutral axis, the bolrload will bedecreasing, This will tend to open upthe joint sooner. On the compiessionside of the neutral axis. the bolt-loadwill be increasins.3 This rvill tend tocrush the gasketlooner.

Assuming that the no-pressure, no-moment bolt-load is (As Son)o, andthat when internal pressure is applied,I/K of the hvdraulic end tt'ua it"picked up" as a d,ecrease in bolt-load,tlren the bolt-load at a pressure p (withno moment) will be approximately

(Ar S.p)o - (AB S.D). -

IKP

Assuming that this same ratio (f)

130

holds for the effect of moment on thetension and compression sides of theneutral axis, then the adiusted bolt-load on the tension side (with no pres-sure) will be approximarely-

(Ar S.o)u. - (A, S.")" - +-

ffi'J,,;"',l1 :::;:"-.*",,,,, i,,u1'as the summation of the easket stressdue to moment. and a triangular dis-tribution is assumed, this force willequal

corrected for both pressure and mo.ment can then be called

(Ar Sop)prrt: (A" S*)" -I ^ rrc' I l-41f-lK " 4 - KL;TI

and this value used in formula (6),which will become

Fv':

M<

Formula (10) then expresses the max.imum moment not to have leakaee dueto insufficient gasket p."su.", cor.rected for the effect of a change inbolt-load. assuming that the boltiloaddecreasesa when pressure is applied.

In the same manner as tle forego-ing, formula (7) may be reworkedto read

ry (12/(-! \G/4 ( ABS,')" - r ";(; + bm)

1 + _-1 ----_--.-

l! 97-

' 7Gt

' 16K- it=1 (r0)

' Kz'

nGA

$

E;lll r,ntjt:8.'Hti

fii'

fl1#ini

fl{

r G/4

so that the bolt-load corrected foramount on the "tension" side of theneutral axis may be taken as

(A"Son)'.- (AnS"").- 1 [4I\tl"- K L' c-land on the compression side may betaken as

(Ar Sq)u" - (A" S.o)^ + I [4 M I" K L;dJThe bolt.load on the "tension" side.

I-;,N

NOMENCLATURE

Coefficient used to multiply the hydraulic end load to obtain

the change in bolt load [assumed to decrease in formulas(10) and (11)l

Change in bolt length 1

Change in bolt force )Change in momentElastic constant of half the bolt length - #/" =Total Bolt Area X "E"----6tFrsth /,

Gasket Thickness /2Er Elastic constant of the flange-"f/Radian:

Total Bolt Load X Lever ArmResulting Angular Rotation in Radians

AB

AttAMF.

Ec Elastic constant of half the gasket thickness - #/" =Gasket Contact Area X "E"

Petroleum Refiner-Vol. 29, No. 6

1

K

M<pr--9" azGlyn__c iA,S"o).'1624-l

ttrt - Krt'

PTG16K-F r (11)

1l,'K,

Formula (11) then expresses the max-imum moment not to have crushine ofthe gasket, corrected for the effeci ofa change in bolt.load, assuming thatthe bolt-load decreasesa when prissureis applied.

Evaluation of the Change inBolt-Load Factor

has been conveniently defined so

as to permit a simple correction forchange in bolt-load. Off hand it mayappear difficult to evaluate. However,this may be done without too niuchlabor.

Figure 12 shows a segment of theflange rvith loads applied at the gasket,bolt circle, and mean diameter of thepipe. Intitially, it is assumed that theflange has been bolted-up to some ini.tial bolt-load, the bolts have extendedsomewhat, the gasket has compressedsomewhat, the flange has rotatedthrough some angle, and that the valueof Ap" is zero. This is the conditionrepresented by the solid-lined figure.The dashed outline shows the new pic-ture when the load Ap" is given somefinite value. Ac is (half) ihe changein thickness of the gasket (assumingthat the center of the gasket does notmove). A 6 is the change in rotationof the flange.' Inspection of the geometry of thefigure will yield the following results:

An - L 46 -

Aa'- half the chansein length of bolts

Apn- change in bolt-load

The f ollowing equilibrium equationsmay be written:

(Summation of forces)LPern- Aru (L * L'; '- 4ot

(evaluation of change in flange moment)

These equations may be rewritten as:

At" * Eu (L'A + -Ac) - EoAc : 0or Ao (-En

- Ec) * A+ L EB - -AP"and Eo Ao L, - En (L A+

(13)

Ac)(L*Lz):EuAe1 As [EoL,*Er (L*L)] *a+

[_En Lr (L, S L,) _ ""r _ro!

Equations (13) and (J4) may besolved simultaneously to yield the fol-lowing results:

A -A [EnL'(L'+L,)+E']Jc - rP' tp' rp"+ p") + p" g" Ht

(1s)

Comparison With Test DataReference No. 5 contains test data

on the behavior of an experimentalffange when internal pressure is ap-plied. It will be informative to useformula (IB) on this test flange, com'pute the bolt-load change after inter-nal pressure is applied, and comparethe computed value with the actualtest figure. The data on flange C-l ofthis reference is as shown in Table 1.

* Computed from the data in reference.

i Some question can be raised as to what constitutes the"gasket" in al assembly of ihis stifiness.

From this data, using formula (17),

e214960 X.938 X .726-86186 [92 + 496A] + 92:X 4960 X .938',

| - .s6zK\{rhen the internal pressure is 300

psi., the hydraulic end lbad Ap" will be:

Lp.t: "tr /4 G2 p : 'n/,1 (26 7 /8)' X 300

: 170,000 #,lfrom the value of ii computed above,

the change in bolt-load should be:I

ApB :-^-- Ape

:.362X 170,000:61,500 pounds

A4 :Ap. lEelrtlelL+ L)le and mo'

rmula (6),

(10)

:es the max'leakage duegSSUr€, col.r change inhe boltiloads applied.tle forego'

re reworked

L"](16)

lEr (EB * Ec) * Es Eo

I T_4416lrGJ

/9+ u-)\8 t_-!tJ,

;

and, since Ar- L' Ao -

Aa:

\-- ^- tEslrL-ld

-JB- a?F te'tn;+E;)T-E" ilH

By substituting equation (17) inequation (12), it can be determinedthat:

l_10"-K-* 1tl'^

I_-K

Er [Eo L L,- Er][Er (EB + Ea) + Ea Ec L1]

(18)

That value of f may then be used

in formulas (10) and (ll). Inspec-tion of the terms of equation (lB)

tshows that t *"y be either positive

or negative (that the bolt-load mayeither decrease or increase) depend'ing on the relative magnitudes of(EcL,L,) and (Er).

:EsA":Eo(LA+

-A")(12)

where En - stiffness of the bolts- pounds per inch deflection

Sign convention assumes bolt loaddecreases when answer is oositive.

Apc - change in gasket load: EoAc

where P,q - stiffness of gasket

- pounds per inch deflectionSign convention assumes gasket loaddecreases when answer is oositive.

AM : cha{rgg in internal flangeresrstlng moment

:E"Aowhere Er- rotational stiffness of flange

': inch pounds per radianSign convention assumes momentincreases when answer is positive.

Figure 12. Loods on ,nffi

IABLE I

G:26'!4"fEc:4960x106(Assuming E:29r

106, and discounting any oiherflexibilities)

i. 29, No. Iune, 7950-A Gulf . Publishing Company Publicotion

That is, the bolt-load should de.crease by 6I,500 lbs. By comparison,the test values ransed from 46.000 toI 24.000-rhe mean'value being 73.000pounds. Assuming this mean value tobe "correct," the discrepancl. betrveenthe computation and the test is about15 percent, In terms of the many fac-tors that can contribute to this dis-crepancy, the agreement betrveen thevalues is quite good. In terms of"safety-factors" generally employedand the small over-all effect on theleakage envelope. the discrepancy isprol'ablr negligiLle.

Figure 13 shows the effect o" Kof varying each of the stiffness factorsrvhile holding the. others constant. Itwill be seen thatf is not sensitive to

changes in E6, in the neigJhborhood ofthe operating value. That is, the gasketis behaving rather effectively as afulcrum. On the other hand. it is some-what sensitive to changes in Ep andEe. Readers familiar t'ith Reference

No. 5 may note that the value of ]o

that lvould be required bv the test dataincreascs as the irrternal pressure isincreased. This mar in pa rt he ex-

!=I

0. r0

plained by decreasing "twisting stiff-ness" of the flange as flange momentsare increased. The smaller flange stiff-ness-f actor u'ould then make for a

1

greater value of rra -and

thus it can

be seen that the results of the formulasagree rvith ttre trend of the test data.

Use of the FormulasThe general suggestion of this arti'

cle is to use formulas (6) and (7) toconstruct leakage. envelopes ignoring

the influence of -i. The formulas are

easj to apply and should be of accu-racv sufficient for practical design'Evaluation of the various stiffness fac-tors. normalll a somervhat complicatedundertaking. is thereby avoided. It isnossible for the formulas to be eithersomer-hat conservative or somewhatunconservative. Figure 14 has been

constructed to shorv the influence of -"on the leakage envelope. It has beenmade from formulas (10) and (11).for the 8-inch-150-pound flange of the

previous example. i is permitted to

vary from f.50 to .50. The shadedarea in the figure de{ines the question-

able zone. Inspection of the figure willshol'that even for this rvide range of

f values, the results of formulas (6)

and (7) are of good accuracy. Also"it can be demonstrated mathemati-callv that the maximum positive

/r \':value (* rf can have, for any combi.nation of the various stiffness fac-

tors, is ( i:) t.r tnis example, (h)is .25; the . boundary corresponding

/l\to that [*J 'r-alue lies uithin the

lolver part of the shaded area. l,eakageenvelopes constructed using formulas(10t and (11) u,ith u rro.iUu" ({)value taken equal to (rt-r) "'iff af.

\\'a)-s be conservative. If formulas (6)and (.7) place the moment-pressurecondition rvell rvithin the envelope, theproblem is adequatelv solved. If theoperating condition falls close to theextremes of the envelope. formulast l0) and ( l I ) mar I'e used rrirh an

assumed ( l- ) t"t,," not greater than\ !"/

( ;; ) .As a Iast resort. the rarious

,stiffness factors mav be calculated and

Figure l3

HFH2Ats*2,-t{

l.rlI'Ko&F&loN.1

.739

.n5

EB rc,F

.0182

. 6.tn=L3-A

v Lrr-SETTING rn= 0 IN REALITI DEFINES THAI TXE FLANGE WILL SEHAVE AS tLEVER AEOUT THE GASKET N'LCRU}I POIIIT.

SETIIN0 %- o llt REALIII DEFINES A CONSTA$! BOLT-LOAD.

SETTII|G En- 0 IN REALITI DEFII{ES A CONSf,[}ll GASXET L0lD---THEREFORE"THE BOLTS ffUST iE5fu-loof OF TXE LOAD.

@*O-

Petroleunt Refiner-l'-ol. 29, No. 6

{

I

I

I

t:

)a

0

)l-

)'e

re

te

IE

l.c

.n

tn

_ls

rd

,F

o.6 Iune, 1950-A Gulf Pubtishing Cottt'fany Publicotiott

>r

r33

l:il'

20or00o

160rooo

1201000

80,o0o

/+0 rOO0

Figure I4. lnfluence of on Leokoge EnveloPe

be evaluated. And service life charac-

ieristics need correlation l'ith static

"iru.u"t"ti.ti"s. These are but a fen' of

the manl avenues along rr'hich te-

searclt must travel until the llanged

i"i"i ft". been thoroughly explored'' (End ol Part III and series')

I{O'I'DS AND III]}'ERENCNSI l-lrp npl l,,ss rr itl senprill] l'c slnaller ^ftor

"t'i!tXt"itit"T;rs mal' note that ttre terl'lencl'.t "-"."if,t*i""

ot t ott-toad is to exaggeRte;h";;"k; -;;"ss-pattern -under morlent-thtrt

}ii"i:l:.."i,r:t"il"*ilH:"\'l"i.L"lil':tl:';:l:,::1":l*l*'i#,f il;"ll"f ";:X,lf .i'Ji'"i;iii"i"'ii*.ti"j. : p"ot-.i'ty an additional refine-il"iri itr tiris nature ltould be urisleading'i;:',*li'*lli...:":H,1?,,iii.1ii,i,:x,,"?J,L'J'1iobtain suctr high acculilcl-";ij;.;' ;

-;;frs5rr" t'ill have the nesatire

"tt";tt ?t"i'-tlEtti" "t*" or all ternrs inrolv-

,"* *, lhe formula lvill reacl the \:alue ob-

lrrin..l tf rll. I olI-lojr'l.increilscs':l'. B. lios-llpirr. U. H 'lpl'h'rdt lI (l'

(lliIer' "Tcsts ol 1{r'al Exchall€'er Flarlgeg --'l'ransitItions of the -\SIIE, 193E'

6 The readcr mal_ rewrite the tornlulas to use

"Ii instrrad ., i-l i wlri.h t'as used to avoid

('ontusi()ll Nith -q. Labro\\''s lacior'

BIBI,IOGR.{PHYE. O. \\-atcrs, D. B. lvesstrom' Il Il' Ross-

freim. l', S. G' Williams. Forlnulas for Stressesi" fiori.O ]'lange Oonnections -

Transactiotrsot tft" eSlfo,1937. Also I)iscussion' Trans-actions of 1938.

l). B. Rossheim, E. I{' Gebhardt' II' G'Oliver. Tests of rJcat Exchanser FlaDges-Tr.rnsaclions of tl e ASNE, 1938'

'I'hc 1fa:'lor For€ie Clo. Modern Flange L)esign'

Fitst Rcport of the PiI)e Flanges Researeilcn--itf"" r""titution of Me':hanical EnEi-

"""1"1-ij*.""a;nas 1936, volume 132 (British)'

-qecond Report of the Pipe Flaneies Research,',i--il."n -i 1n'.li1qtion of Ifechanical Engi-r"..",

-ilo"""ain€as 1939, \'olume 141 (British)'

S. I-al)row Design of lrlanged Joints-I-nsti-toiinti or tr{e.rha;ical }ln€iineels Proceedings191?, Volume 156 (British)'

Ll. R. Ros-rheirn and A. Ii (l l'Iarkl (iasketT,oading Constants -

tri{echani( al EnBineerlng'Septembcr 1943.

,lf'f-,lSUp Coale for lrnfired I'ressu|e Ves-

Steel Flanges A5-L 13161')

ASA Clode for Pressure I'jl)ing'

I-a

used to correctly evaluate (* ) tntiusins that value in formulas (10) and

{11)". These latter formulas have been

arranged so that the numerical com'putati-ons of (6) and (7) are used' so

ihar calculation labor is reduced'

', ,,i

*r*, '.1.l:&i{."

1.8General Conclusions

The rvriter hoPes that the conclu-sions drawn in this article may stimu-late further research, bring into pub-

]ication anY private test data that maybe availabie, and point a direction forfurther experiment. Despite the f act

that the methods of this article are

rational. the problem is by no means

completelv solved' Additional data on

the elastic and plastic charaeteristicsof gasket material are needed' The

tor.ional effect on the flange of the

non-uniform flange'momenls needs lo

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