Foreword:
American Spiral Pipe Works was organized at the first of the
century to produce spiral riveted pipe. This unique product was
widely used in water supply systems for city aquaducts, surface
mining, and penstocks in this country and overseas. A serious
problem developed with this pipe when flanged joints were required. At that time the flanges were made of cast iron and were
often broken during shipment and fabrication. J. Hall Taylor and
his staff solved this problem by developing processes and equipment to manufacture a superior, virtually unbreakable productthe forged flange. Then under a new name, Taylor Forge and Pipe
Works, the company pressed on to become a leader in flange
manufacturing.
They did not stop with that, but topped their achievement by
developing analytical flange design formulas for industry and Code
use. Professor E. O. Waters of Yale University spearheaded this
work and joined Mr. Taylor to co-author the technical papers which
led into the Taylor Forge publication Modern Flange Design.
Industry immediately accepted this convenient system of flange
design and used it worldwide.
This up-dated version of Modern Flange Design carries on the
tradition with a skillful blend of data, graphics, and text. We sincerely hope that this issue will prove to be the most useful of all.
1
Table of Contents
Foreword
1
Introduction
4
Side-step Designing
5-6
Part A Designs
INTEGRAL. LOOSE • OPTIONAL
WELDING NECK FLANGE DESIGN
,
SLIP-ON FLANGES
RING FLANGES
BLIND FLANGES
REVERSE FLANGES
SLOTTED FLANGES
'.'
UNUSUAL SHAPES
EXAMPLE 1
WELDING NECK FLANGE DESIGN
,
Full Face Design
EXAMPLE 2
13
14
SLIP ON FLANGE DESIGN-FLAT FACED
Face and Gasket
15-16
17
,FACTORSm;y.b
Load and Moment
18
20
HARD AND SOFT GASKETS
Bolts
AREA
SPACiNG
21
21
21
·
Stress
23
24
25
FLANGES
BOLTS
Technical Data
TABLE OF CONTENTS
TABLES AND GRAPHS
BLANK FORMS
Symbols and Definitions
Bibliography
Appendix 1 - F. V, f, FL. VL Program Listing
7-12
8
8
8
10
10
10
11
11
12
'
'
27-47
27
28-34
35-38
40-41
42
43-46
Appendix 11- Bolt Torque Chart
47
Regional Offices
48
3
Introduction
Bulletin 502 was first published in 1938 ~y Taylor
Forge and Pipe Works as Modern Flange. Design.
It has since become a standard reference.manual
for the design of bolted flanges-now called Part
A Flanges by the Code.0 These are defined as
having gaskets wholly within the circle enclosed
by the bolt holes and no point of contact beyond
this circle.' Part A rules limit the analysis to consideration of the flange moment that results from:
•
•
•
•
bolt load
gasket load
face pressure load
hydrostatic end load
The analytical aspect of this bulletin covering Part
A Flanges is based on paper number- FSP-59-4
"Formulas for Stresses in Bolted Flanged Connectlons"," This paper considered the effect of tapered hubs and built on an earlier work by E. O.
Waters and J. Hall Taylor "The Strength of Pipe
Flanqes".? These two papers still form the technical base of the Code rules for flange design.
Later, the authors published the derivation of the
flange formulas in a booklet titled, "Development
of General Formulas for Bolted FlangesY'
This seventh edition covers code revisions
through the winter '78 addenda, includes revised
design formulas for reverse flanges, has a reference-only paragraph with design sheets for full
face designs, adds a bibliography and a computer
program listing for F, V, f, FL , V L , shape factors for
hubbed flanges.
The PVRC Subcommittee on Bolted Flanged Connections and the ASME Subgroup on Openings
cooperatiyely developed design methods for flat
face flanges in metal-to-metal contact. Rules for
()
analyzing identical pairs of such flanges were first
published in Mandatory Appendix II of the 1971
Edition of the Code. These rules give a method of
analysis that satisfies all conditions of equilibrium,
provides for compatibility of rotation and translation between elements (hub and flange), and
accounts for the radial effect of pressure acting
on the pipe, hub and flange. The flanges designed
by these rules were identified as "Part B" to distinguish them from "Part A" flanges.
The theory used as the basis for the rules in the
Code for identical Part B flange pairs was extended on a consistent basis to also cover nonidentical flanges. Because such an analysis is
laborious, a simpler method suitable for analyzing
both identical and nonidentical pairs was developed and published as ASME Code Case 1828:
"A Simplified Method for Analyzing Flat Face
Flanges with Metal-To-Metal Contact Outside the
Bolt Circle." The Case was approved by Council
January 9, 1978, after the rules for Part B flanges
had been transferred from Mandatory Appendix II
to Nonmandatory Appendix Y in the Summer '77
Code Addenda.
The simpler rules of Code Case 1828 resulted from
designing for tangential contact between the
flanges at their outside diameter. Also many of the
assumptions and charts that apply equally to Part
A or Part B flanges were used.
It is beyond the scope of this Bulletin to cover
the design of flat face flanges in metal-to-metal
contact, however, the work leading up to the Case
is fully documented in the open technical literature. For further information refer to bibliography
items6 through 12.
PART A FLANGES: GASKET COMPLETELY INWARD
FROM BOLT HOLES - NO OTHER CONTACT.
{~
.
~
'
CD The
use of "Code" in this manual will specifically mean
ASME Code Section VIII, Division 1.
4
Side'step Designing
Any flange design work costs time and effort, and
leads one to ask, "Is there a way I can sidestep
designing?"
The answer for Part A Flanges is yes-two ways.
One way is to consider that the Code recognizes
the proper use of existing flange dimensional
standards. These are fully prepared and ready to
be specified within the limits of their scope and
rating. The Code incorporates ANSI 816.5 "Steel
Pipe Flanges . . .",13 API 605 "Large Diameter
Carbon Steel Flanges",14 and ANSI 816.1 "Cast
Iron Flanges ... 15."Not included, but designed per
Code rules are lndustry Standards Classes 75,175,
and 350,5 and MSS-SP44 "Pipe Line Flanges."15
Note that the 816.5 ratings above ambient do not
apply to the large diameter MSS-SP44 flanges as
they are intended for use with thin-wall high-yield
strength line pipe. These should be checked for
Code applications; sizes over 36" in Classes 300
and greater were designed using higher than Code
allowed stress levels.
Flanges greater than 24" size that are required to
match valves often must use ANSI 816.1 cast iron
dimensions. This may mean adjustments in material, bolting, and facing. All such changes affect
the rating, and require Code Inspector approval.
He will often ask for supporting calculations.
The other way to sidestep the task of designing
is to call on TAYLOR FORGE for help. When
design calculations must be done, and no standard
is found to satisfy all requirements, we will bid
a custom designed flange. This work is part of the
quote and includes price and delivery, but full
dimensional details are held pending an order.
In the case where only a design calculation is
required, this can be furnished for a nominal
charge that depends on the complexity of the
problem and engineering/ computer time required.
For any Part A design calculation, the following
information is essential:
• type of flange
• shell or pipe dimensions
• design pressure and temperature
• flange material
and this information is very helpful:
• governing code
• media contained
• shell or pipe material
• bolt and gasket material
• facing style-if specified
• corrosion allowance-if required
If the design mates existing equipment, give complete details of facing, drilling, and O.D.
OPTIMUM INFORMATION INPUT IS A TRUE ECONOMV IT SAVES GUESTIONS, GUESSES, AND GOOFS.
You may sidestep Code Case 1828 Flange Design
calculation by using our design/computer services.
The calculation work for Code Case 1828 requires much more effort than Part A because the
flanges behave differently. One flange is influenced strongly by the other since they are in
contact outside the bolt circle; accordingly, calculated stresses are meaningful only when the
interaction is considered in the analysis. As a
result, when we are requested to bid on a custom
job and perform calculations, it is essential that
information on both flanges of the pair be provided. We require a sketch of the assembly showing all dimensions which are known or must be
held. Include flange types, shell or pipe dimensions for each flange, material, type and size of
gasket, design pressure and temperature. If the
flanges are to be tested separately, for example
with a blind cover, this information should be
provided to check adequacy of the flanges for this
situation.
CODE CASE 1828 FLANGE PAIRS ARE DESIGNED
FOR 00 TANGENTIAL CONTACT.
6
Part A Designs
Three types of flanges designed by the rules of Part A are defined
and illustrated by the Code in Paragraph UA-48 and Figure UA-48.
See page 7, Fig. 1-Flange Types. The first type is
INTEGRAL
Integral which means the hub and flange are one continuous structure, either as manufactured from the original material or made so
by full penetration welds. Examples are shown in Figure 1a thru 1d
with loads and dimensions needed for designing. Examine hub details
carefully: go is defined in the Code as the hub thickness at the small
end, but for calculation purposes it equals the wall thickness of the
attached pipe. Then the hub length h extends to the point where the
slope of the hub meets the 00 of the pipe. Thus, go in the design
formulas may be different from go as defined, and h shorter or longer
than the hub length as manufactured.
Note that B = Flange 10 = Pipe 10
Use Design Sheet A, page 35.
LOOSE
Fig.1b
~
....
..
"
h>O
<::"""']<,.--.......1('
Fig.1c
Loose types either have no attachment to the pipe as in Figure 1e,
a lap joint, or have a non-integral structure as shown in Figures 1f
and 1g for slip-on flanges. Threaded and socket-weld are also classed
as loose flanges. Lap joints and threaded flanges transfer loads to
the pipe at or near the face, their hubs act independently of the pipe.
The hubs of slip-ons and socket-welds actually interact with the pipe
but this is disregarded in the analysis. See par. UA-52 in the code.
The hubs have no minimum limit on h or go but values of go < 1.5 t;
and h < go are not recommended. If the hub is too small to meet these
limits, it is best to design per Figure 1d as an integral type. (Hub
thickness gl + t« at the base, and t« at the top.)
=
Fig.1f
=
Note that B 10 of flange-not pipe 10.
Use Sheet B or C, pages 36 and 37.
OPTIONAL
Optional types are constructed in such a way that flange and pipe
act as a unit-similar to integral flanges. Optionals would normally
be designed the same way as integral flanges but when:
go :s; 5/8"
Blgo:S; 300
p:S; 300 psi
Temperature s, 700°F
The designer may choose the simpler approach and design as a
loose type, and thus the term "optional flange." This classification
is a convenience not a necessity, because a flange calculation is
done either as integral or loose.
B
Fig.1g
Fig.1h
For those who are beginning designers, example 1, page
12 and the following instructions point the way for
WELDING NECK FLANGES
Welding Neck Flange calculation. This is a typical design
problem; it shows the formulas and the sequence of
their use. lt lists the most frequently specified material
and facing: ASTM A105 carbon steel flange, ASTM A 193
Grade B7 bolts, 1/16// thick asbestos composition gasket,
and a raised face. The first step is to choose material
for flange, bolts, and gasketY Then select facing type,
facing diameter, and gasket width. Locate the gasket
where it will not interfere with bore or bolts. If this data
is not stipulated in the job specification, look for general
guidance on material capability, facing options, and gasket width in the standards mentioned earlier. 13 ,14,15.
Next compute the loads, required bolting area, and complete block 4..
From Table 1, page 28, choose bolt size, in multiples of
four, in number approximately equal to the flange bore.
For starting hub dimensions setting gl = 2gois suggested,
R&E per the bolt size, and h based on 3:1 minimum hub
slope as required by the Code. It is good practice to draw
the flange section full scale, check the bolt spacing and
proportion the hub so that 1 :'S: 1, and make adjustments
before calculating the moments in block 5.
Fill out block 6 using Table 2, page 29 and the F, V, and 1
graphs. Block 7 follows after trial t is chosen. Use an
"educated" guess from a similar design or
t(trial)
= O.72~~f~
Calculate the stresses in Block 8 and 9. If calculated
stresses are greater than those allowed, increase thickness or adjust hub size until the stresses are satisfactory.
Welding Necks are designed the same way as welding neck flanges but the hub is always straight. This
causes the following terms to be constant for each
design:
go = gl
gO/gl = 1
1=1
F= 0.9089
V = 0.5501
Use Design Sheet A, page 35
SLIP-ON FLANGES
Slip-on Flanges also follow the same procedures as
welding neck flanges except 1 is omitted, F L and V L are
used instead of F and V. The hub may be straight or
tapered and trial gl = 2x pipe wall thickness. The flange
ID is not equal to the pipe 00; allowance is needed to
compensate fOr.Jhe nominal pipe OD and irregularities.
Use Design Sheet B, page 36
9
For those who are beginning designers, example 1, page
12 and the following instructions point the way for
WELDING NECK FLANGES
Welding Neck Flange calculation. This is a typical design
problem; it shows the formulas and the sequence of
their use. It lists the most frequently specified material
and facing: ASTM A105 carbon steel flange, ASTM A 193
Grade B7 bolts, 1/16" thick asbestos composition gasket,
and a raised face. The first step is to choose material
for flange, bolts, and gasket. 17 Then select facing type,
facing diameter, and gasket width. Locate the gasket
where it will not interfere with bore or bolts. If this data
is not stipulated in the job specification, look for general
guidance on material capability, facing options, and gasket width in the standards mentioned earlier. 13 ,14,15.
Next compute the loads, required bolting area, and complete block 4. .
From Table 1, page 28, choose bolt size, in multiples of
four, in number approximately equal to the flange bore.
For starting hub dimensions setting g, = 2gois suggested,
R&E per the bolt size, and h based on 3:1 minimum hub
slope as required by the Code. It is good practice to draw
the flange section full scale, check the bolt spacing and
proportion the hub so that 1 :s: 1, and make adjustments
before calculating the moments in block 5.
Fill out block 6 using Table 2, page 29 and the F, V, and 1
graphs. Block 7 follows after trial t is chosen. Use an
"educated" guess from a similar design or
t(trial)
= 0.72~~f:
Calculate the stresses in Block 8 and 9. If calculated
stresses are greater than those allowed, increase thickness or adjust hub size until the stresses are satisfactory.
Welding Necks are designed the same way as welding neck flanges but the hub is always straight. This
causes the following terms to be constant for each
design:
go = gl
gO/gl = 1
1=1
F= 0.9089
V = 0.5501
Use Design Sheet A, page 35
SLIP-ON FLANGES
Slip-on Flanges also follow the same procedures as
welding neck flanges except 1 is omitted, F L and V L are
used instead of F and V. The hub may be straight or
tapered and trial gl = 2x pipe wall thickness. The flange
ID is not equal to the pipe OD; allowance is needed to
compensate fo~tbe nominal pipe OD and irregularities.
Use Design Sheet B, page 36
9
RING FLANGES
Ring Flanges in this manual are hubless. They may be
loose type or slip-on designed as loose type. Use all the
data and procedures of blocks 1 through 5, as in a welding neck flange. In block 6, only K and Y apply, Since
there is no hub or hub factors, the tangential stress is the
only one to be calculated using blocks 8 & 9.
The calculated flange thickness is the greater of
~MoY
t = .·Sto B
or
t=
~MGY
·S
B
. fa
Use Design Sheet C, page 37
BLIND FLANGES
Blind Flanges in this manual are circular and limited to
those shown in the Code in Figure UG-34 sketches (j)
and (k). Use the load data given in blocks 1 through 5
and dimensions-except thickness-from the matching
flange.
'
diti
G IO.3P
1) 0 pera t mg
con I Ions t = V Sfo
2) Gasket seating conditions t
=G
+
1.9 W m 1 h'G
Sfo GS
/1.9 Wh G
" Sja GS
Use the greater thickness.
When the blind has a grooved facing, t under the groove
must at least equal that required for gasket seating.
Use Sheet 0, page 37
REVERSE FLANGES
Reverse Flanges have the hub at the 0.0. as shown in
Figure 2. For operating conditions H T and h» are negative, and h T may be positive or negative. Add the moin
ments algebraically, then use the absolute value
all subsequent calculations. Use B' to calculate K, and
A to find h.;
IMol
A fourth stress equation ST, tangential stress at B', has
been added for both design conditions. This will often
be the controlling stress.
Use sheet E page 38.
10
.,
SLOTTED FLANGES
Slotted Flanges - The effect of bolt holes on flange
design is not considered in Part A rules, but some flanges
require T-bolts with radially slotted holes. This allows
the bolts to swing out of the way of a cover for quick
opening. The slots destroy the continuity of the outer
boundary and the interrupted fibers can no longer contribute to the ring action. Substitute the diameter of the
circle tangent to the inner edges of the slots for A, and
follow the appropriate standard design procedure. See
Figure 3.
Use Design Sheet A page 35
UNUSUAL SHAPES
Unusual Shapes - Bolted connections must sometimes
be fit into tight spaces where the usual geometry cannot
be applied. In this case, flanges may be made square
or oval with circular bores and are treated as inscribed
circular flanges. Bolt loads and moments, as well as
stresses, are calculated as for other flanges, using a
bolt circle passing through the centers of the outermost
bolt holes. Similar assumptions are in order for ovalshaped and two-bolt flanges departing not too greatly
from the circular. For both types, the bolt spacing should
be checked and an allowance made for maldistribution
of the moment. The spacing factor can be less t'!,an is
required for circular flanges since the metal available
in the corners tends to spread the bolt load and even out
the moment.
Special care is needed when the effective (highly
stressed) part of the hub is interrupted. This may occur
with channel flanges on heat exchangers where large
nozzle openings are located in a portion of the hub.
Here is a case where the moment is introduced uniformly
but it cannot be absorbed evenly. Increased moment or
local reinforcement can help compensate for this condition.
The Code rules for flange design provides an alternate
method of calculating hubs stresses for small diameter
flanges. When the inside diameter is less than 20 times
the hub thickness (20 g,), B I may be used for B in the
formula for longitudinal hub stress, SH. Calculate B I as
follows:
BI
= B + s.
for loose hubbed flanges and integral
flanges where the point corresponding to gIl go
and hi h; falls below the f = 1 line. See the values
of f chart, page 34.
B 1 = B + go for integral flanges where f ~ 1
This option is not shown on sheets A & B - it is quoted
here for reference. See the Code paragraph UA-47.
11
Design Pressure, P
400
Design Temperature
StJo' F
Flange Material
A 105
Bolting Material
o
Corrosion Allowance
Design Temp.,
5/0
Flange
4
LOAD AND BOLT CALCULATIONS
17/ felt)
Hp
= 2b"GmP =
Deslqn Temp., Sb
/?/ Silt!
)..5 t1/t1
Atm. Temp., S.
)"~tJtltl
Wm,
= Hp + H = 4-].).-4/4
Atm. Temp., 5'0
Bolting
CONDITION
")I 7
x
LOAD
Ho = 7f82P/4 =
3.1.--/ (,
Hr = H - Ho =
.d ~
1
;j'
LEVER ARM
ho =
R+
hG = .S(C -G)
t:J )
.l-
hr = .5(R
+
g,
MOMENT
/ . ., f,
.5g,
+
hGI =
"
Mo = Hoho =
/.5S(""
..1-. O).-/, "
Mr = Hrhr
M.
hG = .S{C -
}J-J.-j.)j
G)
6
STRESS CALCULATION-Operating
Long. Hub, Sa = fm./A g,'
K AND HUB FACTORS
K
=
= I. d-..)..
A/B
Radial Fig., SR = f3m./'At'
S,.
z
Tong. Fig., ST = m. Y/ 12 -ISR =
~;':f" .5{SH
+ SRI or .5 (SH + Sri
=
STRESS CALCULATlON- ,ealing
Sf.
;;':..- .5(SH
=0.77
V
f).
=
-;;.04/
y
=
'1.77i
u
=IO.7Lo e=F/h.
ho =
Radial Fig., SR = f3mo/AI'
Tong. Fig., ST =mo Y/I'-ZSR
= 1/.
F
Ie:,).
1000
(}./'i'4
g,/g.
Long. Hub, Sa = fmG/Ag,'
Sf.
c, ff
h/h.
/./jo
,,'8g o
7
STRESS FORMULA FACTORS
+ SRI or .5(SH + Sri
a
=te
(3 =
SLOPE· J:3
r/. "
90= ;/-1-
-y
+I
4/3 te
+J
I.S/
O.7S;
= a/T
= tl/d
O·/.J...o
0./79
ma = Ma/'B = operating
jf:, - j "
;801's
-----.t~-'-'-----G=3J'.lfr
Com pule d_...;.-
_
Date
7- / 7 -7 2
~....:......e....-_
,c(/£-~
300
Design Temperature
75A .f'lIO££ J)t/~t.JM&TGI2-
AJtJ7 8
4
()
Corrosion Allowance
Design Temp.,
Atm. Temp.,
5,. /J pip,?
5,.
Design Temp.,
/5###
s,
"}t!tJtJ
Jt/Ptl
Aim. Temp.,S.
CONDInON
r"Ace #6'8e,i!.-
LOAD AND BOLT CALCULATIONS
Hp
= 2b'1TGmP =
Ht,.
H
=
bG/blG
Am
=grealer of W m,"1 S. or W m,l s, =
I..J. 7C:.
/74tJu
Ab
=
/7·/(1
.;!f,4J4J
W
=.5 (Am + Ab) S. =
+ H'GY =.2-J /fb
Wm2 = b'1TGy
=
Hp
= G"ITP/4=
/ /0
x
9w.)../~
MOMENT
LEVER ARM
Ho
= r8'Pl4 =
ho
=
Hr
= H - Ho =
hr
=
+ 91
.5(R + 91 + hG)
1/
=
,;1-.
7 :;
.)...
p
~
'1:1 Jt1~
/7 .J 90
Mo = Hoho =
7
= Hrhr
Mr
H
M.
LEVER
ARMS
REVERSE
MOMENT
B)(2B ± C) -
h _ (C G -
h'
6 (B± C)
HG= W -
h'~= ~
'7 994-
hG
STRESS CALCULATION-operating
5,.
Long. Hub, SH = m.'/>cg,'
Radiol Fig., SR
_ (A G -
~
H=
= f3mol AI'
Tong. Fig., ST =moY/f-ZSR=
±
h'G
=
Conditions (use M)
'9
C) (2A
6 (e
A)
+
±
C)
4J-/"
6
MG = HGhG " =.J..
I jJ.j
=
T
= /. 7~
/~/J(""
Z
=
hlh.
V,
c,.1/
F,
h.
e=-
'}.59
/'po
g,/9o
d =
!".u4
h. = "Bg.
7
~
VI
A= 3,)./'
1
f-9OO / ffc,"
B=Ur
w
f3
/. 99.);.·3)...4-
=Ie+ I
= 4/3 Ie
+
J
/. / »»
s
= alT
= ,3/d
A
="Y+~
=)..
mo
= Mo/B
=
"Y
=.1'.;.-
h.g.' = /.
STRESS FORMULA FACTORS
/. tlt! "
a
/
F,
;1.!7
=
U
j
9/ P
K AND HUB FACTORS
5 ,,).. :it.
RADIALSTRESS AT BOLTCIRCLE
6MG
SRAD
-;:-~~.,..,
le.?
t' (';TC-nd,)
-.",
?5
=
y
Sf.
/ / tl f.,
K = A/B
/
d-tpO
4;J-4!P&-
WMI=H+Hp+H'P=
LOAD
m=
.1..J.-7
.047
d-t, /
.2--
pI
Face and Gasket
Figures to the right picture a variety of flange facing styles
used in industry. Specific recommendations for facing/gasket
combinations are not within the scope of this manual, but pressure, temperature, thermal shock, cyclic operation, and the
fluid handled should be considered. The various flange standards give valuable suggestions in this area, along with dimensional data.
Two general categories are shown. The first seals by bolt force
squeezing the gasket and this includes raised face, tongue and
groove, ring type joint, male and female, and lap joint. The
tongue face can be made with a small nubbin for extra gasket
grip without bolt load penalty. The nubbin style also reduces
b and is used with metal clad gaskets.
RAISED FACE
TONGUE & GROOVE
Gasket materials used in this first category include the various
sheet stocks of rubber, cork, and asbestos compositions,
metallic-elastomer mixes as the spiral wound, and solid metal
rings made as flat washers or ring-type-joint forms.
RING TVPE .JOINT
The other category is called self-energizing or pressure actuated. This means that initial sealing is achieved by the gasket!
facing geometry without significant bolt load, and the gasket
seating force increases with pressure. O-rings made of elastomer
materials are used most often in this style seal. Calculations for
flanges using such gaskets often omit gasket loads and gasket
seating stresses, W Jf2 , H lI , and W, as being neqliqlbly small.
Metallic self-energizing seals, not shown, are delta ring, double
cone, lens joint, metallic O-rings, API RX and BX ring jolnts.t"
All of these require very fine surface finishes, tight tolerances,
and meticulous care in assembling.
LAP .JOINT
16
MALE & FEMALE
0 RING
FACTORS rn.YJb
The problem of specifying acceptable gasket factors has been a
long-standing concern of the ASME Boiler and Pressure Committees.
m = factor needed to hold a seal under internal pressure,
dimensionless.
y = unit seating load, psi
b = effective gasket width, in.
In 1941, Rossheim and Markl 20 reviewed values then in use, made
changes, presented m and y tables for commonly used gasket materials, and suggested rules for finding b. It was known that m increased
as the initial bolt load was given lower values - when the intitial
pressure was zero m was very high. Therefore, the authors decided
thaty could be the m value required for a bolt load that would seal at
zero internal pressure, and proposed the empirical formula y = 180
(2M - 1)2. Although Rossheim and Markl made no claim other than
they hoped to stimulate research, their m and y values were adopted
by the Code.
Gasket tests show leakage usually happens well before the internal
pressure has relieved the gasket reaction.
Suppose the ratio of the compressive stress of the gasket to the
internal pressure of the fluid trying to escape is designated m' at the
instant when leakage starts, then for a very poor gasket m' would be
a large number. For good quality commercial gaskets it might range
between 3 and 1.5. For a theoretically perfect case a leak would not
start until the fluid pressure just exceeded the gasket pressure, with
m' =1. Assuming that reliable values of m' are available, the equilibrium conditions of Figure 4, can be expressed: bolt load = (fluid
pressure) X (area subjected to fluid pressure) + m' (fluid pressure)
X (area subjected to gasket pressure). In formula form this is
W ml = 1r/4 G2 P + 1r 2b Gmp where W ml is the bolt load (operating).
The first term on the right side is the total hydrostatic pressure load
acting on the effective gasket diameter G, and the second is the
gasket reaction over an annular area 2b wide on the same G. Sealing
theory requires that the load 2b1rGmp be resisted by the gasket when
the internal pressure equals P. But the gasket also resists the total
load, W mt- When pressure P is applied, load 1r/4 G2P is removed and
2b1rGmP remains as the theoretical load required to hold a tight
joint at P.
Fig. 4
Factor m is derived from m' and has an added safety margin. Neither
m or y values have theoretical standing and those now in use are
based on practical experience and some formal experimentation.
They have a direct effect on flange design and have been discussed
for years without reaching fixed values that could be made mandatory.
Many variables are involved, and much time is required to make a
single test.18
At the present time, leakage criteria is getting a "hard look" and
research programs are under study by the Pressure Vessel Research
Committee to determine if m and y values can be set up in relation
to specified leak rates. For example, a joint that held for one minute
without the escape of one drop of water was considered "tight".
This equals a leak rate of 10-3 cc. per second and would not be
. allowed in many industries. Possibly a leakage of 10- 4 cc. per sec.,
corresponding to 6 drops per hour, would be acceptable for liquids,
while 10-5 would be necessary for heavy gas and 10-7 for lethal substances. This concept may lead to multiple listings of gasket factors
for a given material-with a different level of m. and y values assigned
to each leak rate and contained fluid.
Note: Code m, y and b values do not pertain to full face gaskets.
17
The Code requires the analysis of two distinct load systems. The first
is gasket seating - when there is no internal pressure. To achieve
a seal, all facing surface irregularities must be filled with gasket
material. This is done with direct force by bolting the flanges. The
required seating load is represented by: W.>n2 = b7rGy and is illustrated in Figure 5 where the bolt load (seating) is balanced by the gasket
reaction.
The other load system relates to internal pressure and has four forces:
H D - the hydrostatic end force
H T - pressure force on the flange face
H, - the total gasket load required to maintain seal
W - the bolt load
The first three forces work to separate the flange pair. They are
balanced by the fourth, W, which holds the assembly together. This
is illustrated in Figure 6.
The hydrostatic end force H D comes to the flange from the closed
end of the pipe system to which it is welded. The end force reaches
the flange through the hub, and pulls on the ring portion of the flange
mid-hub at its large end if it is a tapered hub,
The fluid pressure force H T acts directly on the face of the flange
where it is exposed. For a gasket covering the entire raised face in
Figure 6, H T would equal zero, but as a conservative allowance,
leakage is assumed to be possible as far as G. The HT force acts on
a circle half-way between B & G.
The gasket load, H, = 2b7rGmP where gasket factor m relates the
required gasket stress at design pressure P to that design pressure.
For example, an m factor of 3 means that the residual gasket stress
at P must be at least 3P for the joint to be tight.
In order to calculate the moment acting on a flange, the forces are
multiplied by the appropriate lever arms which are measured from
the point of force application to the bolt circle. The forces and the
lever arms indicated in Figure 6 are for an integral flange.
The gasket reaction load is generally assumed to decrease as internal
pressure is applied. The actual change is affected by flange rotation,
bolt stretch, and the gasket's ability to resist and recover from compression. Bolt loads frequently change too, for the same reason.
They must be retightened, especially when gasket relaxation or
creep occurs.
All of these variables may be explained by the following illustration.
Let a pair of flanges be represented by two steel bars placed side by
side as in Figure 7, page 20; they are separated by blocks, as shown,
Which represent the gasket, and forces W at the ends of the bars
represent the bolt loads, which are balanced by opposite reactions
at the blocks. Under the action of the "bolt loads" the bars are pulled
together at their ends, the amount of deflection can be calculated
by formulas in engineering handbooks. Consider now two cases:
Fig. 5
luuu!
'---y----J
HO
Fig. 6
HARD GASKETS
Hard Gaskets. The blocks are completely rigid, and the bars deflect.
Before internal pressure is applied, the bolt load balances the gasket
reaction, and pulls the ends of the bars towards each other so that
their separation is reduced as the bolts are tightened. For a cantilever,
the ends of each bar would deflect a distance proportional to Wl13/3,
but due to slight rotation as the bars pivot about the blocks, this is
increased to (WlN3) (l +1.5l2n ). Therefore, in the initial bolt-up,
the nuts are wrenched down until the rod ends are brought closer
together by twice this amount, proportional to (Wl 13/3) (2 + 3l 2
Now, when pressure is applied to the bars between the blocks, equal
in amount to Pl 2 , and tending to spread the bars apart, the "bolt load"
W may be kept constant but the "gasket load" on the blocks is
reduced; this may continue until, in the case of a real flange joint,
leakage occurs. In any event, under the most favorable conditions
P may be increased until, in our illustrative example, the pressure on
the blocks is completely relieved, and Pl 2 = 2W. At this point, calculation of the deflection of the ends of each bar indicates that it is more
than before, the total reduction of space between the bars now being
proportional to (WlN3) (2 + 3l 2/ h + 0.5 (l2/l1) 2). In other words,
in order to maintain full bolt load while internal pressure is applied,
the effective bolt lengths must be shortened by wrenching down the
nuts still further.
w
w
w
w
n ).
SOFT GASKETS
Soft Gaskets. The bars are inflexible, and remain straight and parallel
during all changes of loading. During bolt-up the blocks are compressed a small distance and the rod ends are pulled together the
same amount; the "bolt load" = W. Then when pressure Pl 2 is applied
between the blocks, the "gasket load" can only be relieved by letting
the blocks return to their original thickness; this means that the bars
must be separated by the same amount, from end to end, and the
bolt lengths increased to avoid stressing the bolt beyond the original
value of W.
These illustrations represent two extremes, between which an endless variety of conditions can occur.
eo
Fig. 7
Bolts
AREA
Area. The minimum total bolt area required (Am) equals the larger
of WmIl S; or W"'21 So, where S, is the allowable bolt stress at operating
temperature and So, at ambient. Use Am to select bolt size and number. This is easily done for most flange designs, but thin flanges at
low pressure may require excess bolt area because:
1) Bolt sizes <1/2" are easily overstressed, avoid using them
when possible.
2) The number of bolts should be specified in multiples of four
to guide fit-up and alignment.
3) Bolts must be close enough to hold the seal.
SPACING
Spacing. When a very few bolts will satisfy the Code but give bolt
spacing so wide that leakage may occur, adjust the design by increasing the flange thickness, increasing the number of bolts, or both.
This will help the flange seal the gasket-even between bolts. The
best bolting practice is to combine smallest practical size with minimum spacing to carry the load.
In 1950, Irving Roberts completed a detailed study of the interaction
of bolts, gasket and flanges. 21 Investigating the gasket factor m' and
the relation of bolt spacing to leakage, he recognized that gasket
elasticity distributes the load between bolts. He also derived a bolt
spacing curve in terms of flange thickness, indicating a 5 percent loss
of gasket pressure half way between bolts. Mr. Robert's work leads
to a formula for "normal" bolt spacing when a workable gasket-toflange compression ratio S is used. Normal bolt spacing := tS Y' , where
S := compression of gasket! compression of flange, or E, (gasket
thickness) (flange area)1 E, (flange thickness) (gasket area).
E" E,
:=
modulus of elasticity of flange and gasket, respectively.
B, is the uncertain factor in this formula, but gasket manufacturers
or miscellaneous material tables might be data sources.
I
t
~
The formula for maximum bolt spacing, also recognizes the importance of gasket compression by using m. Maximum bolt spacing :=
2a + 6t I (m + 0.5) It assumes proper load distribution when bolt
spacing = 2a + t. Minimum bolt spacing is controlled by the requirements of nut and wrench clearance-see Table 1, page 28. If special
nuts and wrenches are used to permit very close spacing, the flange
section may be seriously drilled away, and the weakening effect
will not be exposed by Part A analysis, discussed pp. 9-16.
FLANGES
Example 1, Page 12 shows the stresses computed
for Part A flanges. Each stress must be equal or
less than the Code allowable except for the longitudinal hub stress which may reach 1.5 x the allowable. This is permitted because SH is a bending
stress. The formula gives a maximum value which
only exists on the inside and outside surfaces of the
hub, and decreases to zero at a point half way
between. If a slight overstress in the hub causes
yielding, the load shifts to the ring portion of the
flange. The ring is also subjected primarily to bending and thus able to absorb the additional load so
that a new equilibrium within safe limits is established. When localized yielding extends to the point
where the flange and hub cease to act elastically
as an integral structure, the flange takes a permanent set or "dishes" and the joint usually cannot
be disassembled and remade in a satisfactory manner. This is likely to occur when an integral flange
has a thin straight hub because bending stress and
direct pressure stresses must be carried at the
same time. If there is cyclic loading, fatigue, or
operation at high temperature in the creep range,
with the stress above the yield point over a considerable portion of the hub, the use of SH = 1.5 allowable should be reviewed.
It is reasonable to expect that stress concentrations
higher in magnitude could be withstood before the
flange ceases to act elastically but at this time
methods for setting this critical level accurately are
very laborious. These limitations apply to ductile
materials having elongations of 15% or more (in 2")
and yield points of 50% to 70% of the ultimate
tensile strength. High strength materials may have
yield points very close to the ultimate tensile
strength or no observable yield point, and with such
materials the higher hub stress should only be used
after careful consideration.
The existence of localized stresses, stress concentrations, and discontinuity stresses of a relatively
high order in all pressure equipment is well known.
Typical examples are stress concentrations around
nozzle and branch connections, stiffener rings or
flat head attachments. The Code Committees and
the Pressure Vessel Research Committee are currently studying such effects in an effort to arrive at
a better method of evaluating safe limits for design.
It is not likely that any simple answer will be found.
The character of the stress and the area over which
24
it exists must be evaluated in addition to the capacity of the adjacent structure to carry increased load.
The Code accounts for localized stresses by using
compensating factors in the design formulas for
stress.
In flange design, the most obvious example of
stress concentration occurs with hubbed flanges at
the corner where the outside surface of the hub
meets the back face of the flange. Integral flanges
provide for this with a fillet radius that is required
to be 0.25 go minimum - but never less than 0.188 .
inches.
BOLTS
R
J
The allowable bolt stresses listed in the Code may
seem to be too conservative, but they were very
carefully selected by the Committees. Particular
reference was made to stresses in flange bolting.
It was recognized that bolts are often stressed
above the tabulated values, and that relaxation
occurs in many service applications due to creep in
the gasket, flange or bolt material.
Appendix S of the Code distinguishes between the
design value of bolt stress and that which might
actually be needed for both design and test conditions. The initial tightening of the bolts prior to
hydrostatic test may be the most severe load that
they will receive. It is sometimes thought that bolts
stressed 1Y2 times the allowable will pass the test,
but this is not necessarily true. As internal pressure
is applied, flange rotation and gasket properties
may actually lower bolt load. To offset this, the bolts
must be tightened as internal pressure is added, or
there will be leakage. After the test, the flange will
tend to relax to its original flatness, the gasket will
recover a large part of its original thickness, and
the twice tightened bolts may be loaded beyond the
design value. 801t capacity for higher initial loading
is desirable and experience bears this out.
Code allowable bolt streses also account for severe torsion and bending during service. The actual
tension achieved in each bolt is never exactly uniform whether by hand wrenching with plain or
torque wrenches, power driven impact wrenches,
or hydraulic bolt tensioners. Tests show that manual tightening develops bolt stresses as high as
45,000/ ~psi. This indicates why a potential problem exists when bolts Y2" and less are specified.
•J
Allowable bolt stress is related to bolt temperature
and in uninsulated piping the bolts are cooler than
the contained medium. It is suggested that the
higher stresses permitted at lower temperature be
avoided unless reliable test data is available and
specifications permit their use. See ANSI 831.3
Paragraph 301.3.1.
25
Coarse Thread
Series
Threads
Root
per
Area
Sq. In.
Inch
Bolt
Size
a
13
11
10
.126
.202
.302
1
1 '1a
9
8
7
.419
.55\
.693
.551
.728
1 '14
1%
1'12
7
6
6
.890
\.054
1.294
.929
1.155
1.405
Pia
1',4
1 'tIa
5 '17
5
5
1.515
1.744
2.049
1.680
1.980
2.304
2
4 '12
2'14
2'12
4'12
2.300
3.020
3.7\5
2.652
3.423
4.292
'12
Ya
3/4
'til
4
4
= 1.0493 [; + 1.3 (l - ~~
T as below; Y = (1 - v U
where" = K - 1; v = 0.3
V
2)
'Ia
3
14
'A.
Bolt
Spacing
Va
1
1 'I.
.969
1.175
1.383
1Y..
1 '17
1~
1 '1a
\ 'iI.
Pia
I' y,.
1.589
1.796
2.002
2 y,.
2Y..
lY..
1 Va
1 '12
2
27\.
2.209
2.416
2.622
2' y,.
3'1,.
1 '12
R
'y,.
'y,.
Y..
':V,.
'y,.
Va
Va
2Va
1 y,.
1 '1a
'iI.
'iI.
2 Va
1 314
lY..
\ 3/a
0/1.
9A.
'/a
3 '14
3 '17
3Y..
1 Va
2
3 '12
2 'Ia
\ '/a
2'14
2 3/a
PA
Va
3~
2'7'\.
2.828
3.035
3.242
1%
'/a
'/a
4
4Y..
4 '12
3 '1a'
3 '12
3%
3.449
3.862
4.275
4'/4
4 314
2 '12
2
2Y..
.' J/a
' y,.
' y,.
'y,.
5Y..
5Va
2 3/a
29A.
2~
When K ranges less than 1:020, the values of Z, Y,
and V change rapidly and the Interpolation Formulas should be used as follows:
2
E
Maximum
Fillet
Radius
r
Edge
Distance
Across
Corners
'I,.
Z=L+ L+.!....
Radial
Distance
Across
Flats
The values of T, Z, Y, and V in Table 2 have been
computed using Poisson's ratio = 0.3 and cover
1.00 :s; K :s; 5.00. The increments of K are chosen
to provide calculation accuracy that is consistent
with formulas of the Code. Values of T, Z, Y, and V
are listed with three of four significant figures, and
the difference between successive tabulations is
not greater than 1% in the range 1.100 :s; K :s; 5.00.
Linear interpolation is adequate for values of Z, Y,
and V when 1.000 :s; K :s; 1.020 where T is almost
constant.
"
Minimum
Nut Dimensions
2'17
4
2 314
3 y,.
5Y.
2'/a
3 314
4~
When K is beyond the scope of Table 2, or a material with a different Poisson's ratio is required,
calculate T, Z, Y and V according to the following
formulas. These are equal to those in the Code
Figure VA - 51.1 when Poisson's ratio V =0.3.
T
(l - v2)
(l - I')
Z
K2 + 1
K2-1 ; Y
K2 (1
V
V
(K2 - 1)
+
(l
+ v)
K2
= (1- v
2
)
V
+ 4.6052 1 + v [ogIOK) - 1
= 1.04720 (K2 -
I-v
1) (K - 1) (l
+ v)
z
1.91
1.91
1.91
1.91
1.91
y
1000.50 1911.16
500.50 956.16
333.83 637.85
250.50
478.71
200.50
383.22
U
T
Z
Y
2100.18
1050.72
700.93
526.05
421.12
1.031
1.032
1.033
1.034
1.035
1.90
1.90
1.90
1.90
1.90
32.76
31.76
30.81
29.92
29.08
62.85
60.92
59.11
57.41
55.80
69.06
66.94
64.95
63.08
61.32
1.061
1.062
1.063
1.064
1.065
1.89
1.89
1.89
1.89
1.89
16.91
16.64
16.40
16.15
15.90
32.55
32.04
31.55
31.08
30.61
1.91
1.91
I. 91
I. 91
I. 91
167.17
1 ~3.36
125.50
111.61
100.50
319.56
274.09
239.95
213.40
192.19
351.16
301.20
263.7 5
234.42
211.19
1.036
1.037
1.038
1.039
1.040
1.90
1.90
1.90
1.90
1.90
28.29
27.54
26.83
26.15
25.51
54.29
52.85
51.50
50.21
48.97
59.66
58.08
56.59
55.17
53.82
1.066
1.067
1.068
1.069
1.070
1.89
1.89
1.89
1.89
1.89
15.67
15.45
15.22
15.02
14.80
30.17
29.74
29.32
28.91
28.51
1.91
1.91
1.91
1.91
1.91
91.41
83.84
77.43
71.93
67.17
174.83
160.38
148.06
137.69
128.61
192.13
176.25
162.81
151.30
141.33
1.041
1.042
1.043
1.044
1.045
1.90
1.90
1.90
1.90
1.90
24.90
24.32
23.77
23.23
22.74
47.81
46.71
45.64
44.64
43.69
53.10
51.33
50.15
49.05
48.02
1.071
1.072
1.073
1.074
1.075
1.89
1.89
1.89
1.88
1.88
14.61
14.41
14.22
14.04
13.85
28.13
27.76
27.39
27.04
26.69
1.90
1.90
1.90
1.90
1.90
63.00
59.33
56.06
53.14
50.51
120.56
111.98
107.36
101.72
96.73
132.49
124.81
118.00
111.78
106.30
1.046
1.047
1.048
1.049
1.050
1.90
1.90
1.90
1.90
1.89
22.05
21.79
21.35
20.92
20.51
42.75
41.87
41.02
46.99
46.03
45.09
44.21
43.34
1.076
1.077
1.078
1.079
1.080
1.88
1.88
1.88
1.88
1.88
13.68
13.56
13.35
13.18
13.02
26.36
26.03
25.72
25.40
25.10
1.90
1.90
1.90
1.90
1.90
48.12
45.96
43.98
42.17
40.51
92.21
88.04
84.30
80.81
77.61
101.33
96.75
92.64
88.81
85.29
1.051
1.052
1.053
1.054
1.055
1.89
1.89
1.89
1.89
1.89
20.12
19.74
19.38
19.03
18.69
38.68
37.96
37.27
36.60
35.96
42.51
41.73
40.96
40.23
39.64
1.081
1.082
1.083
1.084
1.085
1.88
1.88
1.88
1.88
1.88
12.87
12.72
12.57
12.43
12.29
24.81
24.52
24.24
24.00
23.69
1.90
1.90
1.90
1.90
1.90
38.97
37.54
36.22
34.99
33.84
74.70
71.97
69.43
67.11
64.91
82.09
79.08
76.30
73.75
71.33
1.056
1.057
1.058
1.059
1.060
1.89
1.89
1.89
1.89
1.89
18.38
18.06
17.76
17.47
17.18
35.34
34.74
34.17
33.62
33.04
38.84
38.19
37.56
36.95
36.34
1.086
1.087
1.088
1.089
1.090
1.88
1.88
1.88
1.88
1.88
12.15
1l.02
11.89
11.76
11.63
23.44
23.18
22.93
22.68
22.44
1.88
1.88
1.88
1.88
1.88
11.52
11.40
11.28
11.16
11.05
22.22
21.99
21.76
21.54
21.32
24.41
24.16
23.91
23.67
23.44
1.151
1.152
1.153
1.154
1.155
1.86
1.86
1.86
1.86
1.86
7.16
7.11
7.07
7.03
6.99
13.86
13.77
13.69
13.61
13.54
15.23
15.14
15.05
14.96
14.87
1.242
1.244
1.246
1.248
1.250
1.82
1.82
1.82
1.82
1.82
~.69
4.65
4.62
4.59
4.56
9.08
9.02
8.95
8.89
8.83
1.88
1.88
1.88
1.88
1.88
10.94
10.83
10.73
10.62
10.52
21.11
20.91
20.71
20.51
20.31
23.20
22.97
22.75
22.39
22.18
1.156
1.157
1.158
1.159
1.160
1.86
1.86
1.86
1.86
1.86
6.95
6.91
6.87
6.83
6.79
13.45
13.37
13.30
13.22
13.15
14.78
14.70
14.61
14.53
14.45
1.252
1.254
1.256
1.258
1.260
1.82
1.82
1.82
1.81
1.81
4.52
4.49
4.46
4.43
4.40
8.77
8.71
8.65
8.59
8.53
1.88
1.88
1.88
1.88
1.88
10.43
10.33
10.23
10.14
10.05
20.15
19.94
19.76
19.58
19.38
22.12
21.92
21.72
21.52
21.30
1.161
1.162
1.163
1.164
1.165
1.85
1.85
1.85
1.85
1.85
6.75
6.71
6.67
6.64
6.60
13.07
13.00
12.92
12.85
12.78
14.36
14.28
14.20
14.12
14.04
1.263
1.266
1.269
1.272
1.275
1.81
1.81
1.81
1.81
1.81
4.36
4.32
4.28
4.24
4.20
8.45
8.37
8.29
8.21
8.13
1.88
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
9.96
9.87
9.78
9.70
9.62
9.54
9.46
9.38
9.30
9.22
19.33
19.07
18.90
18.74
18.55
18.42
18.27
18.1 J
17.97
17.81
21.14
20.96
20.77
20.59
20.38
20.25
20.08
19.91
19.75
19.55
1.166
1.167
1.168
1.169
1.170
1.85
1.85
1.85
1.85
1.85
6.56
6.53
6.49
6.46
6.42
12.71
12.64
12.58
12.51
12.43
13.97
13.89
13.82
13.74
13.66
1.278
1.281
1.284
1.287
1.290
1.81
1.81
1.80
1.80
1.80
4.16
4.12
4.08
4.05
4.01
8.05
7.98
7.91
7.84
7.77
1.171
1.172
1.173
1.174
1.175
1.85
1.85
1.85
1.85
1.85
6.39
6.35
6.32
6.29
6.25
12.38
12.31
12.25
12.18
12.10
13.60
13.53
13.46
13.39
13.30
1.293
1.296
1.299
1.302
1.305
1.80
1.80
1.80
1.80
1.80
3.98
3.94
3.91
3.88
3.84
7.70
7.63
7.57
7.50
7.44
1.87
1.87
1.87
1.87
1.87
9.15
9.07
9.00
8.94
8.86
17.68
17.54
17.40
17.27
17.13
19.43
19.27
19.12
18.98
18.80
1.176
1.177
1.178
1.179
1.180
1.85
1.85
1.85
1.85
1.85
6.22
6.19
6.16
6.13
6.10
12.06
12.00
11.93
11.87
11.79
13.25
13.18
13.11
13.05
12.96
1.308
1.311
1.314
1.317
1.320
1.79
1.79
1.79
1.79
1.79
3.81
3.78
3.75
3.72
3.69
7.38
7.32
7.26
7.20
7.14
1.87
1.87
1.87
1.87
1.87
8.79
8.72
8.66
8.59
8.53
17.00
16.87
16.74
16.62
16.49
18.68
18.54
18.40
18.26
18.11
1.182
1.184
1.186
1.188
1.190
1.85
1.85
1.85
1.85
1.84
11.70
11.58
11.47
11.36
11.26
12.86
12.73
12.61
12.49
12.37
1.323
1.326
1.329
1.332
1.335
1.79
1.79
1.78
1.78
1.78
3.67
3.64
3.61
3.58
3.56
7.09
7.03
6.98
6.92
6.87
6.04
5.98
5.92
5.86
5.81
~0.21
39.43
y
K
T
K
T
Z
Y
U
K
T
Z
Y
1.131
1.132
1.1 33
1.134
1.135
1.87
1.87
1.86
1.86
1.86
8.16
8.11
8.05
7.99
7.94
15.79
15.68
15.57
15.46
15.36
17.35
17.24
17.11
16.99
16.90
1.202
1.204
1.206
1.208
1.210
1.84
1.84
1.84
1.84
1.84
5.50
5.45
5.40
5.35
5.31
10.65
10.56
10.47
10.38
10.30
11.71
11.61
11.51
11.41
11.32
1.354
1.358
1.362
1.366
1.370
1.77
1.77
1.77
1.77
1.77
3.40
3.37
3.34
3.31
3.28
6.57
6.50
6.44
6.38
6.32
1.136
1.137
1.138
1.139
1.140
1.86
1.86
1.86
1.86
1.86
7.88
7.83
7.78
7.73
7.68
15.26
15.15
15.05
14.95
14.86
16.77
16.65
16.54
16.43
16.35
1.212
1 214
1.216
1.218
1.220
1.83
1.83
1.83
1.83
1.83
5.27
5.22
5.18
5.14
5.10
10.21
10.12
10.04
9.96
9.89
11.22
11.12
11.03
10.94
10.87
1.374
1.378
1.382
1.386
1.390
1.77
1.76
1.76
1.76
1.76
3.25
3.22
3.20
3.17
3.15
6.27
6.21
6.16
6.11
6.06
1.141
1.142
1.143
1.144
1.145
1.8t>
1.86
1.86
1.86
1.86
7.62
7.57
7.53
7.48
7.43
14.76
14.66
14.57
14.48
14.39
16.22
16.11
16.01
15.91
15.83
1.222
1.224
1.226
1.228
1.230
1.83
1.83
1.83
1.83
1.83
5.05
5.01
4.98
4.94
4.90
9.80
9.72
9.65
9.57
9.50
10.77
10.68
10.60
10.52
10.44
1.394
1.398
1.402
J .406
1.410
1.76
1.75
1.75
1.75
1.75
3.12
3.10
3.07
3.05
3.02
6.01
5.96
5.92
5.87
5.82
1.146
1.147
1.148
1.149
1.150
1.434
1.438
1.442
1.446
1.450
1.86
1.86
1.86
1.86
1.86
1.74
1.74
1.74
1.74
1.73
7.38
7.34
7.29
7.25
7.20
2.89
2.87
2.85
2.83
2.81
14.29
14.20
14.12
14.03
13.95
5.56
5.52
5.48
5.44
5.40
15.71
15.61
15.51
15.42
15.34
6.10
6.05
6.01
5.97
5.93
1.232
1.234
1.236
1.238
1.240
1.83
1.83
1.82
1.82
1.82
4.86
4.83
4.79
4.76
4.72
9.43
9.36
9.29
9.22
9.15
10.36
10.28
10.20
10.13
10.05
1.414
1.418
1.422
1.426
1.430
1.75
1.75
1.75
1.74
1.74
5.77
5.72
5.68
5.64
5.60
1.85
1.86
1.87
1.88
1.89
1.56
1.56
1.56
1.55
1.55
1.83
1.81
1.80
1.79
1.78
3.33
3.30
3.27
3.24
3.22
3.65
3.62
3.59
3.56
3.54
2.92
2.95
2.98
3.02
3.06
1.22
1.22
1.21
1.20
1.19
3.00
2.98
2.96
2.94
2.91
1.27
1.26
1.25
1.25
1.24
1.92
1.90
1.88
1.86
1.83
1.454
1.458
1.462
1.466
1.470
1.73
1.73
1.73
1.73
1.72
2.80
2.78
2.76
2.74
2.72
5.36
5.32
5.28
5.24
5.20
-'.89
5.85
5.80
5.76
5.71
1.90
1.91
1.92
1.93
1.94
1.54
1.54
1.54
1.53
1.53
1.77
1.75
1.74
1.73
1.72
3.19
3.17
3.14
3.12
3.09
3.51
3.48
3.45
3.43
3.40
3.10
3.14
3.18
3.22
3.26
1.18
1.17
1.16
1.16
1.15
1.23
1.23
1.22
1.21
1.21
1.81
1.79
1.77
1.75
1.73
1.475
1.480
1.485
1.490
1.495
1.72
1.72
1.72
1.72
1.71
2.70
2.68
2.66
2.64
2.62
5.1·6
5.12
5.08
5.04
5.00
5.66
5.61
5.57
5.53
5.49
1.95
1.96
1.97
1.98
1.99
1.53
1.52
1.52
1.51
1.51
1.71
1.70
1.69
1.68
1.68
3.07
3.05
3.03
3.01
2.98
3.38
3.35
3.33
3.30
3.28
3.30
3.34
3.38
3.42
3.46
1.14
1.13
1.12
1.11
1.11
1.20
1.20
1.19
1.19
1.18
1.71
1.69
1.67
1.66
1.64
1.500
1.505
1.510
1.515
1.520
1.71
1.71
1.71
1.71
1.70
2.60
2.58
2.56
2.54
2.53
4.96
4.92
4.88
4.84
4.80
5.45
5.41
5.37
5.33
5.29
2.00
2.01
2.02
2.04
2.06
1.51
1.50
1.50
1.49
1.48
1.67
1.66
1.65
1.63
1.62
2.96
2.94
2.92
2.88
2.85
3.26
3.23
3.21
3.17
3.13
3.50
3.54
3.58
3.62
3.66
1.10
1.09
1.08
1.07
1.07
1.18
1.17
1.17
1.16
1.16
1.62
1.61
1.59
1.57
1.56
1.525
1.530
1.535
1.540
1.545
1.70
1.70
1.70
1.69
1.69
2.51
2.49
2.47
2.46
2.44
4.77
4.74
4.70
4.66
4.63
5.25
5.21
5.17
5.13
5.09
2.08
2.10
2.12
2.14
2.16
1.48
1.47
1.46
1.46
1.45
1.60
1.59
1.57
1.56
1.55
2.81
2.78
2.74
2.71
2.67
3.09
3.05
3.01
2.97
2.94
3.70
3.74
3.78
3.82
3.86
1.06
1.05
1.05
1.04
1.03
1.16
1.15
1.15
1.15
1.14
1.55
1.53
1.52
1.50
1.49
1.55
1.56
1.57
1.58
1.59
1.69
1.69
1.68
1.68
1.67
2.43
2.40
2.37
2.34
2.31
4.60
4.54
4.48
4.42
4.36
5.05
4.99
4.92
4.86
4.79
2.18
2.20
2.22
2.24
2.26
1.44
1.44
1.43
1.42
1.41
1.53
1.52
1.51
1.50
1.49
2.64
2.61
2.58
2.56
2.53
2.90
2.87
2.84
2.81
2.78
3.90
3.94
3.98
4.00
4.05
1.03
1.02
1.01
1.009
1.002
1.14
1.14
1.13
1.13
1.13
1.48
1.46
1.45
1.45
1.43
1.60
1.61
1.62
1.63
1.64
1.67
1.66
1.65
1.65
1.65
2.28
2.26
2.23
2.21
2.18
4.31
4.25
4.20
4.15
4.10
4.73
4.67
4.61
4.56
4.50
2.28
2.30
2.32
2.34
2.36
1.41
1.40
1.40
1.39
1.38
1.48
1.47
1.46
1.45
1.44
2.50
2.48
2.45
2.43
2.40
2.75
2.72
2.69
2.67
2.64
4.10
4.15
4.20
4.25
4.30
.996
.989
.982
.975
.968
1.13
1.12
1.12
1.12
1.11
1.42
1.40
1.39
1.38
1.36
1.65
1.66
1.67
1.68
1.69
1.65
1.64
1.64
1.63
1.63
2.16
2.14
2.12
2.10
2.08
4.05
4.01
3.96
3.92
3.87
4.45
4.40
4.35
4.30
4.26
2.38
2.40
2.42
2.44
2.46
1.38
1.37
1.36
1.36
1.35
1.43
1.42
1.41
1.40
1.40
2.38
2.36
2.33
2.31
2.29
2.61
2.59
2.56
2.54
2.52
4.35
4.40
4.45
4.50
4.55
.962
.955
.948
.941
.934
1.11
1.11
1.11
1.10
1.10
1.35
1.34
1.33
1:31
1.30
1.70
1.71
1.72
1.73
1.74
1.63
1.62
1.62
1.61
1.61
2.06
2.04
2.02
2.00
1.99
3.83
3.79
3.75
3.72
3.68
4.21
4.17
4.12
4.08
4.04
2.48
2.50
2.53
2.56
2.59
1.35
1.34
1.33
1.32
1.31
1.39
1.38
1.37
1.36
1.35
2.27
2.25
2.22
2.19
2.17
2.50
2.47
2.44
2.41
2.38
4.60
4.65
4.70
4.75
4.80
.928
.921
.914
.908
.900
1.10
1.10
1.09
1.09
1.09
1.29
1.28
1.27
1.26
1.25
1.75
1'.76
1.77
1.78
1.79
1.60
1.60
1.60
1.59
1.59
1.97
1.95
1.94
1.92
1.91
3.64
3.61
3.57
3.54
3.51
4.00
3.96
3.93
3.89
3.85
2.62
2.65
2.68
2.71
2.74
1.30
1.30
1.29
1.28
1.27
1.34
1.33
1.32
1.31
1.31
2.14
2.12
2.09
2.07
2.04
2.35
2.32
2.30
2.27
2.25
4.85
4.90
4.95
5.00
.893
.887
.880
.873
1.09
1.09
1.08
1.08
1.24
1.23
1.22
1.21
1.58
1.58
1.58
1.57
1.57
1.89
1.88
1.86
1.85
1.84
3.47
3.44
3.41
3.38
3.35
3.82
3.78
3.75
3.72
3.69
1.80
1.81
1.82
1.83
1.84
Z
U
TABLE UA-49.1
GASKET MATERIALS AND CONTACT FACINGS 1
Gasket Factors (m) for Operating Conditions and Minimum Design Seating Stress (y)
Gasket
Factor
m
Min.
Design
Seating
Stress
0
0
.. ,
0.50
1.00
0
200
«:»
2.00
2.75
3.50
1600
3700
6500
~
1.25
400
/J
3-ply
2.25
2200
~
2-ply
2.50
2900
I-ply
2.75
3700
1.75
1100
·LJ
2.50
3.00
10,000
10.000
~
~
Gasket Material
Se lf-Energi zing Types
o Rin~s, Metallic, Elastomer other gasket types
cons i ered as self-sealing
Elastomers without fabric or a high percentage of
asbestos fiber:
Below 75A Shore Durometer
75A or higher Shore Durometer
I~
thick
'I,. thick
';'. thick
Asbe sro s with a suitable binder for
the operating conditions
Elastomers with cotton fabric insertion
Elastomers with asbestos fabric insert ion , with or without wire reinforcement
---.Vt"I!;!'lable fiber
----
Spiral-wound metal, asbe-stos filled
Corrugrn e d
metal, as-
I
Carbon
Stainless or
Monel
y
Sketches
and
Notes
2900
3700
4500
5500
6500
Corrugated metal
Soh aluminum
Soft coppE'r or brass
Iron or soft s te e]
Monel or 4-6% chrome
Stainless steels
2.75
3.00
3.25
3.50
3.75
3700
4500
.5.500
6500
7600
Fla!. trlPlal jacketed asbe s t os fi led
Soft aluminum
Soft copper or brass
Iron or soft steel
Monel
4-6% chrome
SteinlE'ss steels
3.25
3.50
3.75
3.50
3.75
3.75
5500
6500
7600
8000
9000
9000
Grooved metal
Soft aluminum
Soft COppE'r or bras s
Iron or soft steel
Monel or 4-6% chrome
Stainless steels
3.25
3.50
3.75
3.75
4.25
5500
6500
7600
9000
10100
Solid flat metal
Soft aluminum
Soft COppE'r or brass
Iron or "oft steel
Monel or 4-6% chrome
Stainless steels
4.00
4.75
5.50
6.00
6.50
8800
13000
18000
21800
26000
e:»
Ring joint
Iron or soft steel
Monel or 4-6% chrome
Stainless steels
5.50
6.00
6.50
18000
21800
26000
~~
---'-
--"
...
...
(Ia),( Ib).
( le),(ld).
(4),(5)
}II
(la).(1b)
~
~
~
~
~
.,
~
(I a),(1 b),
(le),(ld)
(la),( Ib).
(Ie). '( Id),'
(2)'
(1a),(lb).
(11:).(ld).
(2).(3)
~
NOTES:
(I) This table gives a list of many commonly used gasket materials and contact facings with
suggested design values of m and y that have generally proved satisfactory in actual service
when using effective gasket scaling width b given in Table UA-49.2. The design values and
other details given in this table are suggested only and are not mandatory.
(2) The surface of a gasket having a lap should not be against the nubbin.
'From ASME Code Section VIII Div. 1-Reprinted by permission.
Refer to Teble UA-49.2
.:»
2.50
2.75
3.00
3.25
3.50
or
Corrugated metal, jacket ed asbestos fi led
Use
Column
~
Soft aluminum
Soft copper or brass
Iron or soft stee l
Monel or 4-6% chrome
Stainless steels
hes to s inserted
Use
Facing
Sketch
(Ia),( Ib).
(I c),(l d),
(2).(3).
( 4),(5)
""\
'1
(6)
."
TABLE UA-49.2
EFFECTIVE GASKET WIDTH
Basic Gasket Seating Width, bo
Column II
Facing Sketch
(Exaggc:ralt,d)
(13)
(lb)'
««llll(ltlll
~
~
{({u¢CJ~~
Column I
~
l\\\\S'f
~
CSSSSS1
~
~
~
~
..L~
(2)
~
1/64 in. Nubbin'
(J)
1/64 in. NUbbin
(4)'
~
~.(W+N
max)
2'
4
<.N
W <: N
w
t:':;;:::
-r ..
.
~
wrN
<!!....
=
·L;N:.I
<:.
W
rT ; (W+N
--2- 4 - max )
w~
3N
8
N
N
2
3N
8
4
«<f1'<"~~t(Cd'
WWW
~
--
3N
8
-7N
N
3N
8
16
"Y'UIdd$"U'
~
(6)
w -to
-4-
2
~
(5)'
2
"~N:rm
~
( III)'
s.
2
~
~
w'~..iT w
(1t)
J:!....
~u.,(,~
4
~
1 wt-
~
-w
8
Effective Gasket Scatin~ Width. "b"
b = bc" when bo ~ X in.
b ,jTJ;; h b
1/ •
= 2' w
en
n
> /4
In.
Location of Gask ..t Load R..action
H~I_
GThc-,
l
Gasket
Face
.
NOTE: The gasket
factors listed only
apply to flanged
joints in which the
gasket is contained
entirely within the
inner edges of the
bolt holes
NOTE:
( I) WI",rc· serrations do not exceed 1/64 in. depth and 1/32 in. width spacing, sketches (lb) and
(Ill) shall be: used.
FL. [UA-51.4]
VALUES OF
VALUES OF VL [UA-51.6]
z0
/5
.ee
,
.
."
0
.or ~
.00
."
...
/00
-
./.
40
-
30
i
.'0
.-"'./2
./0
r--
.'0
.
'0
.14f--.Ih
I--
.25
J8
.20
.'"
4
-
2S
"
.3D
.as
.'0
e
.>5
--=
I--
.. 7<>
.,,,
l..,
....
0
5
.<0
,
.8
'--
.""
c------,
7
h
Zoo
.80
I
.0'
I--
~
h
h. "
,.
1-.11
h
'"rr- I- ho"ra;.
.
I.e>
/
.'iJ
~
... ---= ==-
-
.80 ~
,
.0
- -
.00
1.50
-
.00 " ' - .
5
.oe
4
1.0
'.0
40
/.5
VALUES OF f [UA-51.6]
zs
I
1.5
Z
4
3
5
Z5
eo
20
./ ./
/
/
/s
./
/
/
/5
/
V
/
/ V / V /
/
/ 1/ / /
10
/1/
.,
/0
1/
/
9
/
/1/
/
8
/
/
1/
/
i/ /
7
/
1/
1/
~~o
6
4
/
/
1/
/
/
/
/
/
/
1/
/
/
e.s
2.5
./
/
2
/
/
/
/
/
2
·7
/
/
/
/
/
1/
/
V
/ 1/ /
/ / V
/
/
/
/
/
/
V
/
/
/
1/
/
/
/
1.5
1/
l.Uj
/
/
V
z·
,-v
/
/
/ 1/ /
1.5
1/
/
/
/
/
/
/
V/ /
/ 1/
V/ /
/
/
V
/
/
/
/
/
1/
1/
/
/
1.5
/
1/
/
/
/
/
.5
4
1/
/
/
/
V
.~/
/
7
1/
/
1/ V
8
/
//
/ /
/ / 1/ / / /
1/ / / / / /
V
V 1/
~o
/
fl
/
/
1/
I~j
1/
/
4
1
5
N=
Design Pressure, P
b=
Design Temperature
G=
Flange Malerial
y=
m=
4
Corrosion Allowance
LOAD AND BOLT CALCULATIONS
Design Temp., Sfo
Flange
Atm. Temp., Sfo
= 2b1TGmP =
H.
• =
Design Temp., Sb
Bolling
Atm. Temp., S.
Wml
CONDITION
LOAD
Ho = 1<8'PI4 =
ho =
hG
Operating HG =Wm,-H =
Hr= H -
= H. + H =
x
Ho =
hr
MOMENT
LEVER ARM
R+ .5g 1
Mo = Hoho =
= .51C -G)
= .51R
MG = HGhG
+ g, + hG)
=
Mr = Hrhr
M,
hG = .51C -
STRESS CALCULATION-Operating
Sf,
Sf,
Long. Hub, 59
=
GI
6
KAND HUB FACTORS
= AlB
fm./Ag,"
K
Radial Fig., SR = [3m,/At"
T
F
z
v
Tang. Fig., ST
=
m, YI I" -ZSR
=
hlh,
y
Sf.
STRESS CALCULATlON- .ealing
long. Hub, 59
u
e = Flh.
= fmG/}.g,"
Radial Fig., SR = [3mG/At"
Tang. Fig., ST
~:.::- .5(SH
= mG Y/1" -ZSR
7
STRESS FORMULA FACTORS
+ 5.) or .5(SH + SrI
a
I_ _jl~
h=
A=
-Io'i4f--""-----+'lt----B=
t=
~8olts
----I~-----'-------G=
=te
{3 =
+J
413 Ie
+I
A
= alT
= 13/ d
=-y+o
mo
= Mo/ B = aperaling =
me
= MG/B = sealing =
-y
0
GASKET
FACE
N=
b=
G=
y=
Bolting Material
I
m=
4
Corrosion Allowance
Design Iemp.,
LOAD AND BOLT CALCULATIONS
W m 2 = b.. Gy
5/0
5,.
Hp
= 2b .. GmP =
Design Temp., Sb
H
=- G' .. P/4
Atm. Temp., S.
Wm,
=
Aim. Temp.,
CONDITION
Hp
+
=
H =
x
LOAD
HD = ."B'P/4 =
= R+
hI
=
.5(R
MD = HDhD
g,
hG = .51C -
HI = H-HD=
MOMENT
LEVER ARM
hD
G)
+ gl + ltd
MI = Hlhl
M.
hG = .51C -
G)
6
STRESS CALCULATION-Dperating
me /Ag,'
K
= 13m. /AI'
T
Long. Hub, SH =
5,.
5,.
Radial Fig., 5,
Tang. Fig., Sr =
K and HUB FACTORS
=
A/B
h/h.
z
m. Y/1' - ZS,
v.
y
STRESS CALCULATION- Sealing
<;,.
Long. Hub, SH
=mG/Ag,'
Radial Fig., 5,
= 13mG/AI'
Tang. Fig., SI = mo Y/" -
1 ~~,
'.-E=
t--!
f3
= 4/31e
+
= a/T
I'
Ii
= ,'/d
A =1'+0
mo =
MO/
B= OPERATING =
mG = MG/ B = SEATING.=
W
h=
STRESS FORMULA FACTORS
= Ie + I
a
HD
II
h.
7
ZS,
~A=
F,
e=-
u
R=
9J=
B=
t=
c=
!4------G=
Compuled
_
Oale
_
3
FROM Fig. UA·49
N=
Delig" Pressure; P
b=
G=
y=
Bolting Material
m=
4
Corrosion Allowance
LOAD AND BOLT CALCULATIONS
Design Temp., 5'0
W m 2 = b1rGy
Atm. Temp., S'D
Hp
Flange
= 2b1rGmP =
Design Temp., Sb
Baiting
Atm. Temp., So
Wml
CONDITION
=
x
LOAD
HD =
+H=
Hp
LEVER ARM
...8'P/4 =
nD
= .5(C -
nG
= .51C - Gl
n, =
H,=H -HD =
nG
w
~--c=
~A=
-
,------ I
h-t-B=
MD
+ loG)
.51 ho
6
=
HDnD
M, =H,n,
= .51C - G)
MG
SHAPE CONSTANTS
K
=
A/8
y=
+
If bolt spacing exceeds 2a
t, multiply
M o and MG in , equalions by,
D
t=
,
MOMENT
B)
7
OPERATING
G=
~
t=
GREATER
OF
t=~
M,Y
Sfn B
N=
Design Pressure, P
b=
Design Temperature
G=
y=
Bolling Material
m=
4
Corrosion Allowance
Design Temp.,
LOAD AND BOLT CALCULATIONS
W m 2 = b .. Gy
5'0
Flange
Atm. Temp., S'G
Hp
= 2b1rGmP =
Wml
=
Design Temp., Sb
Bolting
Atm. Temp., So
Hp
+H=
Thickness Calculations
t=G
Operating
[0.3P
'J
Thickness =
Greater of
+ 1.9Wm,ho
sr, G'
Sfo
r----=
NOTES
1. 00, Facing, drilling. Gasket-same as matching
flange-if any.
2. Na additianal thickness is required for facing
special design B.F:s.
3. Unless otherwise specified, faces af blind flanges
gasketing.
_
A= _
w . .-----
c=
-H4--'--t-----G=
~8olt5
.51C - G)
may be machined only over area required for
Sealing
r
nG =
Date'
_
Number
_
G=C -
Design Pressure, P
Design Temperature
2hG =
y=
m=
4
Corrosion Allowance
Design Temp., Sfo
Flange
LOAD AND BOLT CALCULATIONS
Wm.= b'ITGy
Atm. Temp.,
+ H'GY =
Am = greater of Wm.!S. or Wm,fSb =
Hp =2b'ITGmP =
5,.
W = .5 (Am
+ Ab) 5. =
Design Temp., 5b
Baiting
Aim.Temp., 5.
WMI = H
x
LOAD
HD = 7(82P14
+ Hp + H'p =
=
LEVER ARM
MOMENT
= R + 91
hT = .5(R + 91 + hG)
MD
hD
Hr=H-HD=
=
HDhD
MT = HrhT
M.
+
h _ (C - B)(2B C) G 6(B
C)
LEVER
ARMS
+
REVERSE
MOMENT
h' G = (A - C) (2A
6(C+A)
+ C) =
HG=W-H=
MG
6
STRESS CALCULATION-Dperating
= m"n\"g,'
Fig., SR = pm.I>.t"
K AND HUB FACTORS
Long. Hub, Sn
K = AlB
Radial
T
z
Tong. Fig., ST=m.Y/t"-ZSR=
::aa,:i .5(SH + s.l or .5 ISH + ST)
y
=
U
RADIAL STRESS AT BOLT CIRCLE
SRAD
6MG_
t'('lTC-nd ,)
Sf.
7
A=
1
f-~'
a
STRESS FORMULA FACTORS
=Ie+ I
f3 = 4/3
"Y
s
B=
h=
w
t-~
t=
L~~~~
14--±------+----c=
-.t......- - - - - - G =
'Bolts
= HGhG" =
Ie
= alT
=I'/d
>.
="Y+[,
m.
=
M./B
+
SYMBOLS & DEFINITI.ONS
Part A is a type of flange having the gasket wholly
within the circle of the bolt holes and no contact
beyond that circle
Part B isa type of flange with metal-to-metal contact
outside th~ bolt circle, identical pairs only
Code Case 1828 Flanges: Type with metal-to-metal
contact outside the bolt circle having identical or
non-ldentlcal pairs, & designed by the simplified
rules of cc 1828.
A
a
= nominal bolt diameter, in.
.a
aR
= alpha -
stress formula factor, te + 1
= alpha
stress formula factor,
= .!. [1+3(K+l)(1-v)]
b
shape factor; for integral flanges e =
F/h o, for loose flanges e = Fdh o
hub shape factor for integral flanges
hub shape factor for loose flanges
1
hub stress-correction factor for integral
flanges, when the chart reading gives
values < 1 use 1
G
diameter at location of gasket load reaction,
in. Except as noted in sketch e of Figure 1,
G is defined as follows:
When bo ~ Y4 in., G = meah diameter of
gasket contact face
When bo > Y4in., G = outside diameter
of gasket contact face less 2b
go
= thickness of hub at small end, in.
gl
= thickness of hub at back of flange, in.
= gamma-stress formula factor=a/T, a/Tn
for reverse flanges.
H
= inside diameter of flange, in. When B is
less than 20 glJ it is optional for the designer
to substitute B 1 for B in the Code formula
for longitudinal hub stress BH .
HD
HG
total hydrostatic end force
= tr/4 G2P,
Ibs.
= hydrostatic end force on area inside of
flange = To/4 B2P,lbs.
gasket load, operatlnq H, = W",1 - H, Ibs.
= gasket load, seating = W, Ibs.
e
= B + gl for loose hubbed flanges and also
flG
.. for integral flanges when 1<1
B + go for integral flanges when
H;
= total joint-contact-surface compression
load = 2brr GmP = W m 1 - H, Ibs.
H»
= difference
h
= hub
h»
= radial distance from C to the circle on which
I~ 1
= effective
gasket or joint-contact-surface
seating width, in.
= effective
b;
= basic
{3
= Beta ~ stress formula factor = 4/3 te
C
= Bolt-circle diameter, in.
gasket or joint-contact-surface .
pressure width, in.
d
40
= t3 / d
FL
y
2b
d,
=
7TY
for reverse flanges
B1
F
R -
K2.
B
= hub
cross-sectional area of bolts at
root of thread or section of least diameter
under stress, in.2
total required bolt cross-section area, in. 2
=
stress formu la factor
radial distance from C to A, in.
e
= actual total
Am
= delta -
E
= outside diameter of flange. For slotted
flanges the diameter of the circle tangent
to the inner edge of the slots, in.
Ab
Il
=
gasket seating width, in.
+1
between total hydrostatic end
force and the hydrostatic end for an area
inside of flange = H - H D , Ibs.
length, in.
H D acts, in.
ho
= radial distance from G to C =
(C - G)/2, in.
hub shape factor, for integral flanges d =
U ho go2, for loose flanges d _ U hogo2, for
V
VL
reverse flanges d = Un h o go2
V
b,
= factor =
h»
= radial distance from C to the circle on which
Bolt hole dia.
K
~Bgo, in.
H; acts, in.
= A/B, A/B' for reverse flanges
'0
"-
= lambda -
mo
= MolB -
ma
= MalB-unit load, seating, MoIB' for re-
stress formula factor
= y + Il
unit load, operating, MoIB' for reverse flanges, Ibs.
verse flanges, Ibs.
MD
=
component of moment due to H v
inch-pounds
= HDhD,
M a = total moment acting on the flange, seating
= Wha, inch-pounds
Ma
= component of moment due to H 0, operating
=Hah inch-pounds
= total moment acting upon the flange, for
G,
Mo
operating conditions, inch-pounds.
M p = component of moment due to H T = HTh T
m
N
U
U R = K -tactor for reverse flanges
V
hub shape factor for integral flanges
VL
hub shape factor for loose flanges
w
width used to determine the basic gasket
seating width b o, based upon the contact
width between the flange facing and the
gasket (see Table UA-49.2), in.
W
flange design bolt load for operating or
seating conditions, as may apply, Ibs.
Wml= required bolt load, operating conditions, Ibs.
Wm2= min. req'd. bolt load for gasket seating, Ibs.
Y
YR
= gasket factor
width, used to determine the basic gasket
seating width b.; based upon the possible
contact width of the gasket, in.
n
number of bolts
v
Nu -
P
design pressure, psi
R
radial distance from bolt circle to point of
intersection of hub and back of flange for
integral and hubbed flanges, in.
= K-factor
y
K-factor
= K -factor for reverse flanges
= gasket or joint-contact-surface unit
seating
load, psi
Z
= K-factor
Poisson's ratio = 0.3 for steel
radial distance from bolt circle to bore, ring
flange, in.
Sa
= allowable bolt stress at atmospheric temperature, psi
Sb
allowable bolt stress at design ternp., psi
Sfa
SH
SR
Sp
0
= allowable
design stress for material of
flange, nozzle neck, vessel or pipe wall, at
atmospheric temperature, psi
= calculated longitudinal stress in hub,
psi
calculated radial stress in flange, psi
calculated tangential stress in flange, psi
T
K-factor
TR
K-factor for reverse flanges
t
flange thickness, in.
t;
pipe wall thickness, in.
4"1
BIBLIOGRAPHY
1. Pressure Vessels, ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, Appendix 2.
2. Waters, E. 0., Wesstrom, D. 8., Rossheim, D. 8., and Williams,
F. S. G., "Formulas for Stresses in Bolted Flanged Connections,"
Trans. ASME, Volume 59, 1937, Pages 161-169.
3. Waters, E. 0., and Taylor, J. H., "The Strength of Pipe Flanges,"
Mechanical Engineering, Volume 49, Mid-May 1927, Pages 531542.
4. Waters, E. 0., Rossheim, D. B., Wesstrom, D. B., and Williams,
F. S. G., Development of General Formulas for Bolted Flanges,
Taylor Forge and Pipe Works, Chicago, Illinois, 1949.
5. Taylor Forge Catalog 571.
6. Schneider, R. W., "Flat Face Flanges with Metal-to-Metal Contact
Beyond the Bolt Circle," Journal of Engineering for Power, Trans.
ASME, Series A, Vol. 90, No.1, Jan. 1968, pp. 82~88.
7. Waters, E. O. and Schneider, R. W., "Axisymmetric, Non-identical,
Flat Face Flanges with Metal-to-Metal Contact Beyond the Bolt
Circle," Journal of Engineering for Industry, Trans. ASME, Series
B, Vol. 91, No.3, Aug. 1969, pp. 615-622.
8. Waters, E. 0., "Derivation of Code Formulas for Part B Flanges,"
WRC Bulletin No. 166, Oct. 1971.
9. Schneider, R. W. and Waters, E. 0., "Some Considerations Regarding the Analysis of Part B Code Flanges -1974," ASME
Paper No. 75-PVP-48, 1975.
10. Schneider, R. W. and Waters, E. 0., "The Background of ASME
Code Case 1828: A Simplified Method of Analyzing Part B
Flanges," Trans, ASME, Journal of Pressure Vessel Technology,
Vol. 100, No.2, May 1978, pp. 215-219.
11. Schneider, R. W. and Waters, E. 0., "The Application of ASME
Code Case 1828," Trans. ASME, Journal of Pressure Vessel
Technology, Vol. 101, No.1, February 1979, pp. 87-94.
12. A Simplified Method for Analyzing Flat Face Flanges with Metalto-Metal Contact Outside the Bolt Circle, ASME Code Case 1828.
13. Steel Pipe Flanges and Flanged Fittings, ANSI Standard B16.5.
14. Large Diameter Carbon Steel Flanges, API Standard 605.
15. Pipe Line Flanges, MSS-SP44.
16. Cast Iron Flanges and Flanged Fittings, ANSI Standard B16.1.
17. Kent, G. R. "Selecting Gaskets for Flanged Joints," Chemical
Engineering, May 27,1978.
18. Raut, H. D., and Leon,G. F. "Report of Gasket Factor Tests,"
WRC Bulletin 233, December 1977.
19. Specification for Wellhead Equipment 6A, American Petroleum
Institute.
20. Rossheim, D. B. and Markl, A. R. C. "Gasket-Loading Constants,"
Mechanical Engineering, September, 1943, pp. 647-648.
21. Roberts, I. "Gaskets and Bolted Joints," Journal of Applied
Mechanics, Trans. ASME Vol. 17, June, 1950, pp. 169-179.
42
APPENDIX I
o
Computer Program Listing That Calculates F, V, f, F1" V L
This program was written by E. C. Rodabaugh of Battelle Memorial
Institute and his permission to reprint is gratefully acknowledged.
The program is based on formulas developed in reference (4).
Minor editorial changes have been made to publish the listing in this
manual. The program was adapted to run on a 370/145 under as.
c
CALCULATE FLANGE FACTORS, F, V , SMALL-F, F-SUB-L, AND V-SUB-L
OET(OI1,012,013,D21,D22,D23,031,D32,033) =
1 011*022*033 + 012*023*031 + 013*032*021
2 -( 031*'022*013 + 032*023 *011 + 033*012*021)
50 REAO (5,I,ENO=100)
GIGO, HHO
1 FORMAT (2EI0.5)
C GIGO= GIIGO, HHO = H/SQRT( B*GO)
10 CONTINUE
A = GIGO -1.
B = 43.6B*HHO**4
AL PHA,
B = KAPPA
C A
PRINT 2, GIGO, HHO
2 FORMAT (9H
G lIGO= , 1PIEIO.5,BH
H/HO=, 1E10.5/n
A2 = A*A
A3 = A**3
011=1./3.+ A/12.
C1l= 011
012=5./42. + 11.*A/336.
C12=012
013=1./210. + A/360.
C13=013
o14= 11 ./360 • + 59.*A/5040. + (1.+3.*A) IB
C14=014
015=1./90. + 5.*A/I008. - (1.+A)**3/6
C15=015
016=1./120. + 17.*A/5040.
1.1 B
C16=016
021=C12
C21=021
022=215./2712. -+ 51.*A/1232. + (60.17.
225.*A/14.
1
5.*A3/2.) I B
75.*A217.
C22=022
023= 31./693 O. + 128.*A/45045.
(6./7.
15.*AI1.
12.*A2/7.
1
5.*A3/11.) I B
C23=023
024=533./30240.
653.*4/73920. + H./2. -+ 33.*4114 •
1
25.*A3/84.) 1 B
39. *A212 8.
C24=024
025=29./3180.
3.*AI704. - (1./2. .. 33.*A/14.
81.*A2I28.
1
13.*A3/12. ) I B
C25-025
;:
.
..
..
..
..
..
.
..
.
.
. .
..
..
43
1
026=31./6048.
15.*A2128.
.
C26=026
031=C13
C31=031
032=C23
C32=032
C32=032
033=1./2925.
..
1763.*A/665280.
*"
5 .~A3/42.) I B
.
11.*AI300300.
..
1 + 156.*A2 1 385. + 6.*A3/55. )
..
(l
./2 • .. 6.*A/7.
(8./35.
1 B
..
18.*A/35 •
C33=033
+ (1./35.
034=761./831600.
*" Q37.*A/1663200.
3.*A3/70.1 I B
1 + 11.*A2/70.
.
C34=034
035=191./415800. + 103." A133264 c.
A3/10.) I B
1
17.*A2/70.
- u
.
.
C35=035
036=233./831600. + 97.*A/554400.
2.*A3/105.) I B
1 +A2I14.
..
..
*"
6.*A/35.
./35. +6.*A/35.
( 1./35.
.
3.*A/35.
C36=036
DETI = OET(OI1,012,D13,02l,D22,D23,D31,D32,D33)
011=C14
021=C24
031=C34
OAIAAO = DE r r 011 ,012,013 ,021 , D2 2,023,031,032,033 I
011=C15
021:::C25
031=C35
OAIAAI ::: OETIOl1,012,013,021,022,023,031,032,0331
011=C16
021=C26
031=C36
OA1BBO = OET(011,012,013,021,D22,023,0~1,032,0331
011=C11
021=C21
031=C31
012=C14
022=C24
032=C34
OA2AAQ = OETtOl1,012,013,021,022,023,031,032,033)
012=C15
022'=C25
032=C35
OA2AAI = DET(Dl1,012,013,021,022,023,031,D32,D33)
012=C16
022=C26
032=C36
OA2BBO = OET(Dl1,012,OI3,D21,022,023,031,032,033)
012=C12
022=C22
032=C32
013=C14
023=C24
033-=C34
OA3AAO = DET(Dll,D12,013,021,022,D23,D31,D32,033)
013=C15
44
o
023=C25
03 3=C3 5
OA3AAl = DETlOl1,D12,013,D21,D22,023,D31,032,033)
013=C16
023=C26
033=C36
OA3BBO = OETtDl1,012,013,021,022,023,031,032,033)
AlAU=OA 1 AAO 10 ETl
A1Al=OA1AAl/OETl
AIBO=OA1BBO/OETl
AZAO=OA2AAO/OETI
AZA l=OA 2AA I/0ET 1
A21:30=OA26BO/OETI
A3AO=OA3AAO/OET1
A3Al=OA3AAl/OETl
A3BO=OA38BO/OETl
C ABOVE COMPLETES DETERMI NATIUN OF AI, AZ , AND A3 IN TERMS OF AA1,AAO,BBO
Cll=Ol1 -{B/4.l**.25
012=-5./12. - AlAO + A2AO - (B/4. )**.25*A1AO
C12=012
013=-1./12. - AIBO + A2BO - (B/4.)**.25*A1BO
C13=013
021= -{B/4.)'t*.5
C21=021
022=1./2.
CZZ=022
023= o.
C23=023
031= -{1:3/4.1**.15
C31=031
032= 3.*A/2. + {B/4.)**.7S*A1AO
C32=032
033=1./2. + (B/4.)**.7S*AIBO
C:; 3= 033
DET 1
= OET(OI1,C12,D13,021,D22,023,031,D32,D33)
AIAl
Al = 1./12. + ALAI - A2Al + (8/4.)**.25
A2 = o.
A3 = - (8/4.)**.75
ALA 1
011 = Al
021 = A2
031. = A3
De5
= OETtD11,012,013,021,022,023,031,032,033.
011 = Cll
021 .: C21
031 .: C31
012 = Al
022 = A2
032 .- A3
DAD
= OETIOll,012,013,021,022,023,031,D32,0331
012 = C12
022 = C22
032 = C32
013 = Al
023 = A2
033 = A3
:;;
OBD
OETlOll,012,013,021,D22,023,031.D32,0331
*
*
45
/
DC5 = DCS/DETl
DAD = DAD/DEll
DBU = DBOIOEll
PRINT 5, De5, DAG, DBO
S FORMAT (IP3E15.5/n
Al = A1 AI]Jf'D AO ... A 1A 1 + AIBO*D30
A2 = A2AO*LJAO + A2A 1 ... A213Q*OBO
A3 = A3AO*DAD + A3Al + A3~O*OBO
THETA = -Ai -3.*A212. - A3/5. ... OAO/4. +- 1./4. +- OBO/12.
PI -:: (1.12.+A/6. >*.\1 ... ll./4 .... 11.*A/84.)*A2 +- (1./70.+-A/I05.)*A3
1 -(7./120.+A/36.+3.*A/B)*OAO - (1.140. +- AI12.) - 1I./60. +2 A/120. +- 1./B)*060
F = -Pl/{(B/2.73)**.25
(1.+A)"*3 1 B)
V = THETA I ( (2. 731 B) **. 25
* (1.+AI"'·3)
FS = DAD I (l.+A)
C LOOSE HUB FLANGE, AAO ;; BBO -= a
060=0.
OAO=DBO
Al = AIAO*OAO + ALA 1 ... AleO*D60
A2 = A2AD*DAO + A2A I + A2BO*OBO
A3 = A3AO*DAO + A3A 1 + A3BO*DBO
THETA = -AI -3.*A212. - A3/5. ... OAO/4. + 1./4. +- OBO/12.
PI -:: (1./2.+A/6.'*Al ... (1./4.+11.*A/S4.I*A2 + (1.170.+A/I05.)*A3
1 -(7./120.+A/36.+3.*A/B)*OAO - (1./40. + A/l2. ) - (1./60. +
2 A/l20. ... 1./BI*OBO
FL = -Pl/«B/2.73}.*.25
tl.+AI**3 I B)
VL = THETA I ( (2 • 73 1 S) .:fC . 2 5* (1.+-A)··3)
PRINT 3, F, V, F S, Fl, VL
F= , 1PIE 1 o , S, 5H
\J.= , lEIO.5,
3 FORMAT ( 5H
F-SUB-l=, IEIO.5,
SMALl- F=, lE10.5, l,llH
1 llH
V-SUB-L=, lElO.5,/ln
2 llH
GD TO 50
100 CALL EXIT
END
*
.
48
APPENDIX II
BOLT TORGUE CHART
0··- •
Torque in Foot-Peunds for
Various Bolt Stresses
Machine
and
Cold-rolled
Steel
Alloy
Steel
Per in.
Root
Dia.
in.
Root
Area
in. 2
20
18
16
14
13
12
11
10
9
8
7
7
6
6
5 1/2
5
5
4 1/2
0.185
0.240
0.294
0.345
0.400
0.454
0.507
0.620
0.731
0.838
0.939
1.064
1.158
1.283
1.389
1.490
1.615
1.711
0.027
0.045
0.068
0.093
0.126
0.162
0.202
0.302
0.419
0.551
0.693
0.890
1.054
1.294
1.515
1.744
2.049
2.300
Nominal
Dia.
Threads
in.
1/4
5/16
3/8
7/16
1/2
9/16
5/8
3/4
7/8
1
1 1/8
1 1/4
1 3/8
1 1/2
1 5/8
1 3/4
1 7/8
2
1/4
5/16
3/8
7/16
1/2
9/16
5/8
3/4
7/8
1
1 1/8
1 1/4
1 3/8
1 1/2
1 5/8
1 3/4
1 7/8
2
2 1/4
2 1/2
2 3/4
3
20
18
16
14
13
12
11
10
9
8
8
8
8
8
8
8
8
8
8
8
8
8
0.185
0.240
0.294
0.345
0.400
0.454
0.507
0.620
0.731
0.838
0.963
1.088
1.213
1.338
1.463
1.588
1. 713
1.838
2.088
2.338
2.588
2.838
0.027
0.045
0.068
0.093
0.126
0.162
0.202
0.302
0.419
0.551
0.728
0.929
1.155
1.405
1.680
1.980
2.304
2.652
3.423
4.202
5.259
6.324
7500 psi
1·
2
3
5
8
12
15
25
40
62
98
137
183
219
300
390
525
563
15000 psi
2
4
6
10
15
23
30
50
80
123
195
273
365
437
600
775
1050
1125
30000 psi
4
8
12
20
30
45
60
100
160
245
390
545
730
875
1200
1550
2100
2250
30000 psi
45000 psi
60000 psi
4
8
12
20
30
45
60
100
160
245
355
500
680
800
1100
1500
2000
2200
3180
4400
5920
7720
6
12
18
30
45
68
90
150
240
368
533
750
1020
1200
1650
2250
3000
3300
4700
6600
8880
11580
8
16
24
40
60
90
120
200
320
490
710
1000
1360
1600
2200
3000
4000
4400
6360
8800
11840
15440
The torque values above are suggested only due to the many variables
that affect actual results. These loads are based on the use of heavy
oil-graphite lubricant and the thread forms shown. Efficiency of nonlubricated bolts may drop 50%. More accurate bolt tension is calculated as follows: Divide total elongation by the bolt length, and
multiply the result by E, the modulus of elasticity. Bolt length is taken
mid-nut to mid-nut, or an equivalent distance. Careful micrometer
measurements are required.
47