-
Table 10. Finite element analysis data from Reference r 261 on
run moments (branch moments shown for comparison)
c ~ (a) c (b) ~1ode l R/T r/R t/T tn/T r/rp rz/tn 2r
Mor H. Mtr Mob Hi.b Mtb Lr UA 50.5 0.5 0.5 0.5 0.990 1.00 1. 10
4.62 4.35 16.6 7.00 1. 39
B 40.5 0.5 0.5 0.5 0.998 1.00 1.09 4.54 4.18 15. 1 6.54 1.32 c
20.5 0.5 0.5 0.5 0.976 1.00 1. 05 4.09 3.53 10.8 5.17 1. 2 5 D 10.5
0.5 0.5 0.5 0.955 1.00 1.04 3.60 3.41 5.77 3.28 1. 39 E 5.5 0.5 0.5
0.5 0.917 1.00 1.03 3. 1 7 2.79 3.50 2.64 1. 43 F' 5.5 0.08 0.08
0.08 0.917 6.25 1.04 3. 11 2.12 l. 27 1.36 1.02
SlA 50.5 0.5 0.5 4.34 0.861 0.500 1.04 2.19 2.98 11. 1 2.19 1.
16 B 40.5 0.5 0.5 4.01 0.843 0.500 1.04 2.23 2.87 9.84 2.09 1.16 c
20.5 o.s 0.5 3. 14 0.780 0.500 1.04 2.25 2.43 5.64 1. 51 1. 17 D
10.5 0.5 0.5 2.45 0.705 0.500 1.04 2.07 2. 11 2.81 1.42 1 1 6 E 5.5
0.5 0.5 1. 92 0.623 0.500 1. 03 2.07 1. 70 1. 56 1. 49 1. 1 3 F
20.5 0.32 0.32 2.56 0.732 0.500 1.04 2.36 2.01 2.56 1.22 1.06 G
10.5 0.32 0.32 1.98 0.649 0.500 1.04 2.23 1. 92 1. 43 l. 37 1.07 H
5.5 0.32 0.32 l. 52 0.563 0.500 1.03 2.08 1.68 1.39 1. 37 LOS I
20.5 0.16 0.16 1. 88 0.646 0.500 1. OS 2.49 1.81 1.22 1. 2 3 1.02 J
10.5 0.16 0.16 1.43 0.555 0.500 1.04 2.38 l. 78 1.26 1.25 1.02 K
5.5 0.16 0.16 1. 08 0.468 0.500 1.02 2,33 1. 64 1.33 1. 32 1.03 L
20.5 0.08 0.08 1.38 0.551 o.soo 1.06 2.52 1.76 1.18 1.22 1.01 H
10.5 0.08 0.08 1. 03 0.459 0.500 1. 04 2.61 l. 7 5 1. 18 1. 21 1.
01 N 5.5 0,08 0.08 0.72 0.391 0.500 1.03 2.63 1.68 1 21 1.20
1.02
E'30A 50.5 0.32 0.32 3. 19 0.808 0.500 1.03 2.24 2.30 3.73 1. 19
1.08 B 20.5 0.32 0.32 2.13 0.743 0.500 1.04 2.39 2.13 1.84 1,24
1.08 c 10.5 0.32 0.32 1. 60 0.695 0.500 1. 03 2.27 1.97 1.39 1.32
1.07 D 5.5 0.32 0.32 1.23 0.659 0.500 1.03 2.05 1. 7 3 1.33 1.35
1.05 E 5.5 0.08 0.08 0.533 0.556 0.938 1. 03 2.68 1. 72 1. 19 1. 20
1. 01
(a) c # 2r = a/ (H/Z ) r (b) Czb = o/(M/Zb)
can be written as i9liu = 3.75[(t/T)/(r/R)] 112(r/rP).
Now, as an upper bound to i9/i11 the ratio (t/T)/(r/R) is not
likely to exceed 5, r/R is not permitted to exceed 0.5 and r/rp
cannot exceed 1.0. Accordingly,
(ig/ill)max = 3.75 X 5 X 0.5 112 X 1.0 = 13. This means that use
of Eq. (9) instead of Eq. (11) might result in an overestimate of
i-factors for check-ing run ends by a factor of up to 13.
To bound possible underestimates, (t/T)(r/R) is not likely to be
less than 1.0 and r/rp is not likely to be less than 0.5. Then i
9/i 11 will be less than 1.0 if r/R is less than (1/1.875) 2 =
0.284. However, even for R!T = 50 the maximum underestimate is by a
factor of 1.544 and this factor decreases to 1.50 at r/R = 0.213
because both i9 and i 11 are equal to their lower bounds.
Accordingly, the effect of including Eq. (11) in ANSI B31.1 for
"Branch connections" will almost al-ways be to reduce the
conservatism in checking the run ends.
4.5 Combination of Moments Up to now, we have been discussing
the accuracy of
i-factors for individual moments. In piping systems, a branch
connection will be subjected to the nine mo-ments indicated in Fig.
3. Let us suppose that we could determine accurate SIFs for each of
the three individ-ual branch moments, balanced by one end of the
run pipe. Then we might estimate the combined fatigue-effective
stress by:
SE =[i()M() + i,M, + itMtl/Zb (32) or by
S - [(' M )2 ('M)2 (' M )2]1/2/Z E - La o + ti i + 1t t b (33)
Equation (32) is an upper bound because it assumes that the maximum
fatigue stress due to each of the three moments occurs at the same
point on the branch connection and lies in the same direction so as
to add algebraically. However, we know that fatigue usually
initiates near the longitudinal plane for M 1b, but near the
transverse plane for Mob Equation (33) has a theo-retical
foundation for straight pipe but for branch
Stress Intensification Factors 25
-
Table 11. Finite element and strain gage data on run moments
(branch moments shown for comparison)
Ref. no.
25
23
Hodel Hethod R/T
ORNL-1 F. E. S.G.
ORNL-2 F.E. S.G.
ORNL-3 F.E. S.G.
ORNL-4 F.E. S.G.
1 S.G. 2 s.G. 3 S.G. 4 S.G.
49.5
49.5
24.5
24.5
20.7 12.4
7.6 5.7
r/R
0.49
1. 00
0.111
0.125
1.00 1.00 1. 00 1.00
t/T
0.50
1. 00
0.84
0.32
1.00 1.00 1. 00 1. 00
2.7 2.3 5.9 4.5 1 1 1.2 1. 0 1.3
3.68 2.58 1.68 1. 72
C ' (a)
5.7 3.8
10.1 14.9
2.5 3.2 3.1 4.0
8.03 5.35 3.48 2.87
13.0 10.0 37.5 24.2
5.6 2.5 5.1 5.0
6.8oc 5 .18c 3.55 3.20
37.2 35.3 17.8 15.8
7.3 5.0 7.6 8.5
9.33 6.65 4.14 3.53
c ~ (b)
10.9 10.0 15.2 11.0
5.6 3.7 7.2 6.1
12.14 8.14 4.48 3.92
5. 1 12.5 37.5 31.3 0.6 1.7 1.0 1.5
1 o. 4 9 7.38 4.36 4.53
(a) a/(M/Z ) for M and Mir a/(M/22 ) for H r tr r or
(b)
(c) Maximum and minimum principal stresses have same signs,
except for these two cases: a = 6.68, a i = -6.80 ; a -5.18, a i =
0.23
max m n max m n
connections it only represents a judgmental evalua-tion of the
effect of the three combined moments.
ANSI B31.1 and the ASME Code both combine stresses by:
SE = i[~ + MJ + A(;?jl12/Z (34) To the extent that i = max(i0 ,
ii, i1), which is generally the intent, and for branch connections
where io ii and i 1 are different, then Eq. (34) would be more
conserva-tive than Eq. (33). Both ANSI B31.1 and the ASME Code also
use Eq. (34) for run moments. Calculated values of S E for both the
branch end and the run ends must be less than the Code allowable
stress.
Fig. 14 illustrates a problem in evaluating combined moments.
Figs. 14(a) and 14(c) show the combination of moments for which we
have i/s for branch moments. However, there is an infinity of
possible run moments between (a) and (c) which will balance the
branch moment and which might occur in piping systems, one of which
is shown as (b). Fig. 14(b) is of particular interest because 29720
and Fujimoto21 analyses are based on these run end conditions.
If a fatigue test were run with the end conditions shown in Fig.
14(b), would the resulting ir be different from (a) or (c)? We do
not have any such tests, but would speculate that if r/R is less
than about%, the difference would be small. However, for r/R = 1.0
there might be a difference in that ir for Fig. 14(b) would be less
than for (a) or (c). It is the latter that we have i/s for; hence,
in this sense our i/s may represent upper bounds.
Figs. 14(d) and (e) illustrate other possible moment
combinations. Fig. 14(e) is the pure run moment case for which we
do have some data as discussed in Section 4.4.
Fig. 14(d) illustrates the more complex case; the ASME Code
Class 1 method of separating these into branch moments and run
moments is shown. The total calculated stress is then obtained by
adding the stress-es due to the branch moments to those due to the
run moments. ASME Code for class 2/3 piping and ANSI Codes follow a
conceptually different procedure in that each of the three ends is
checked separately. Comparisons between these two conceptual
methods is discussed in detail in Ref. 27 so we will not discuss it
further except to note that:
1. The conceptual difference is significant only for the type of
moment combinations illustrated by Fig. 14(d).
2. For a narrow range of branch connection parame-ters and
moments, the ASME Code Class 1 meth-od is more conservative by a
factor of up to two.
3. Neither conceptual method can be demonstrated to be accurate
or even relatively more accurate.
4.6 Branch Connection Description Inconsistencies In the quest
for more accurate i-factors, a desirable
Code characteristic is that for a given configuration of branch
connection the Code should give the same i-factors. However, note
the following:
The ASME Code, Class 2/3 piping, for a UFT gives:
26 WRC Bulletin 329
-
Table 12. Run moments, maximum stresses
Table 10 max. Table 11 max.
c2;' ASME c2;' 2i, ASME Hodel 2 X Eq. (ll) 2i, Class 1' Model 2
X Eq. (11) Class 1' max. (4) max. Eq. (4) (a) Eq. Eq. (30) (b) Eq
(30) UA 4.62 5.46 24.6 5.36 25-1 6.5 t 5.28 24.3 5.31
B 4.54 4.72 21.2 5.08 5.0 t 5.28 24.3 5.31 c 4.09 3.00 13.5 4.28
25-2 18.8 t (10.8) 24.3 (5.34) D 3.60 3.00* 8.6 3.62 14.9 (10.8)
24.3 (5.34) E 3.17 3.00* 5.6 3.08 25-3 2.8 t 3.00* 15.2 2. 70 F 3.
11 3.00* 5.6 3.08 3.2 3.00* 15.2 2. 70
25-4 3.1 3 .00* 15.2 3.54 S1A 2.98 t 5.46 24.6 3.13 4.0 3.00*
15.2 3.54
B 2.87 t 4.72 21.2 3.02 c 2.43 t 3.00 13.5 2.71 23-1 8.03 (6.03)
13.6 (4.29) D 2. 11 t 3.00* 8.6 2.65* 23-2 5.35 (4.29) 9.7 (3.78) E
2.07 3.00* 5.6 2.65* 23-3 3.48 (3. 09) 7.0 (3. 34) F 2.36 3.00*
13.5 2.65* 23-4 2.87 (2.55) 5.7 (3.11) G 2.23 3.00* 8.6 2.65* H
2.08 3.00* 5.6 2.65* I 2.49 3.00* 13.5 2.65* J 2.38 3.00* 8.6 2.65*
K 2.33 3.00* 5.6 2.65* L 2.52 3.00* 13.5 2.65* a 2.61 3,00* 8.6
2.65* N 2.63 3.00* 5.6 2.65*
P30A 2.30 t 3.50 24.6 3.02 B 2.39 3.00* 13.5 2.67 c 2.27 3.00*
8.6 2.65* D 2.05 3.00* 5.6 2.65* E 2.68 3.00* 5.6 2.65*
(a) From Table 10, maximum of c 2' for Mar Mir' Mtr' Maximum is
either from Mir or Mtr; where from Mtr' value is followed by a
10t".
(b) From table 11, maximum of c 2; for Mar' Mir or 1/2 of c2;
for Mtr" Maximum is either from Mir or Htr; where from Htr' value
Is followed by a "t",
i(t/T) = [0.9(RITf1~ (tiT), for checking branch (35) i =
0.9(RIT) 213 , for checking run ends (36)
The ASME Code, Class 213 piping, for a "Branch con-nection,"
gives:
ib = 3.0(RIT)213(riR) 112(tiT) (r/r p) ;;::: 2.1 mimimum
(37)
ir = 0.8(RIT) 213(riR) ;;::: 2.1 minimum (38)
We have written Eqs. (35)-(38) so that they are direct-ly
comparable with respect to calculation of S e; i.e., Eqs. (35) and
(37) would be used with Zb Eqs. (36) and (38) would be used with
Zr. We have written Eqs. (37) and (38) for r 2-not-provided [see
Table 1, footnote 6(h)] so that Fig. 2(d) is geometrically
identical to a UFT. The i-factors for i(tiT) for Eq. (35)] for RIT
= 50, riR =tiT, and rlrp = 0.99, are:
r/R =tiT Equation 0.1 0.2 0.3 0.4 0.5
(35) 1.22 2.44 3.66 4.89 6.11 (37) 2.1 3.61 6.62 10.2 14.3 (36)
12.2 12.2 12.2 12.2 12.2 (38) 2.1 2.17 3.26 4.34 5.43
We have discussed the relative accuracy of these SIF equations
elsewhere; our point here is that for geomet-rically identical
branch connections the Code gives different i-factors. A code user,
not recognizing that a UFT with r IR up to 0.5 is also covered by
"Branch connection," might do something unnecessary such as adding
a pad or changing the piping system. The Code would be improved in
this respect by adding a foot-note, tied to UFT's, saying that for
riR ~ 0.5, UFT's can alternatively be evalauted as "Branch
connec-tions."
As indicated in Table 1, ANSI B31.3 incorporates a commendable
effort to distinguish between different
Stress Intensification Factors 27
-
(a) Fatigue Test Moments
-10
(b) Some A.n~tl.ysee Moments
-10
0 _ __,_ __ 10 (c) Fatigue Teat Moments
-10
-1Q __ L 20- (d) Branch and Run Combination -10
+ -10_1_ 10
0
(e) Pure Run Moments 10 -10
Fig. 14-lllustration of combinations of branch and run
moments
types of branch connections. This, in the long run, will provide
improved Code guidance for adequate but not over-costly piping
systems. However, there is an in-consistency between UFT's and the
"Branch welded-on fitting (integrally reinforced)" which merits
some discussion.
First, footnote 7 tied to "Welded-on" reads: "The designer must
be satisfied that this fabrication has a pressure rating equivalent
to straight pipe." Now, there isn't anything simple about
reducing-outlet branch connections so we ask the question: Which
straight pipe, the run or the branch? We think the intent is the
run pipe so that question could be an-swered by inserting the word
"run" before pipe in the footnote. The question then arises as to
how the de-signer meets the requirement of footnote 7. Presum-ably,
the intent is that the designer orders fittings from a manufacturer
with a designated wall thickness (e.g., Sched. 40) with, perhaps, a
requirement in his purchase order that the fitting must have a
pressure rating equivalent to the desired schedule run pipe.
There appears to be a couple of ways the manufac-turer could
assure himself and his customers that his fittings, when properly
welded into designated run pipe, would have a pressure rating
equivalent to the run pipe:
1. Run burst tests. 2. Show compliance with paragraph 304.3 of
B31.3,
using designated wall thickness rather than cal-culated by Eq.
(2) of B31.3.
Now the potential inconsistency arises because UFT's
(unreinforced fabricated tees), if they are to meet B:31.3, must
be reinforced as required by paragraph
304.~3 of B3 U~ for the design pressure. We think that most
UFT's will meet both burst tests and paragraph :304.3 for the
designated wall thicknesses. We note that Table l(f) indicates an
angle like On in Fig. 2(c), but with no control of that angle;
i.e., it could be zero. We presume this omission of a control on 0,
is intentional; i.e., it covers fittings such as indicated by Figs.
2(a) and (b) as well as (c). Our point is that, without a control
on 0,, it may also include UFT's Fig. 2(d). Noting in Table 1 the
differences in h, B31.3 indicates that for geometrically identical
branch connections, we might have SIFs that differ by a factor of
(3.3) 2/:l = 2.2.
4.7 ANSI B16.9 Tees, Sweepolets (Bonney Forge Trade name)
In order to keep this report from becoming even more complex
than it is, we have not given data on ANSI B16.9 tees or
Sweepolets. There is a fairly sub-stantial amount of data on B16.9
tees. Data are avail-able for r!R = 1.0 and for r/R = "'-'0.5; but
nothing in between. Accordingly, we do not know if there is a peak
in the SIF for Mob as suggested by Figs. 6, 7 and 8. At present,
plans are being made to fatigue test some 4 x 3, std. wt. ANSI
B16.9 tees with Mob loadings. These tees have an r/R ratio of 0.77
and should give some indication as to whether a peak does
exist.
Sweepolets in sizes 12 x 6 and 14 x 10, both standard weight,
have been fatigue tested with both Mob and M,b loadings. The r/R
ratio of these two sizes is 0.51 and 0.76, respectively. The Mob
tests indicate that there is a peak somewhere around 0.75. The Mib
tests agree with the general relationship (see Figs. 6-10) that the
it for M;b is much lower than for Mob and there is no significant
peak as a function of r/R. 4.8 Stress Limit, Sx
As indicated by Eq. (12), having calculated SE the Code then
provides a limit; SE.::::: Sx. The stress limit is an important
part of assessing the significance of the accuracy of i-factors.
The Codes prescribe the stress limit, Sx, as:
where f = cycle dependent factor ranging from 1.0 for
7000 cycles to 0.5 for > 100,000 cycles Sc = allowable stress
at cold temperature in cycle sh = allowable stress at hot
temperature in cycle Ss = sum of longitudinal stresses due to
pressure,
weight and other sustained loads. The significance of the stress
limit is discussed in de-tail in Ref. 27. For the purpose of this
report, we make the following observations;
(1) For materials like ASTM A106 Grade B carbon steel at
temperatures up to about 600 F, with S, and S11 from the ASME Code
or from B31.1, there is a margin between failure and Code a!-
28 WRC Bulletin 329
-
lowable moments that ranges from about 8 for 100 cycles of
moments to about 2 for 7000 or more of moments. Many piping do not
undergo more than 100 cycles of full moment range; hence, for those
an un-derestimate of S E by up to a factor of 8 would not
necessarily imply failure.
(2) Observations in (I) are also applicable to aus-tenitic
stainless steel materials like ASTM 312 Type 304 or Type 316.
(3) Observations (1) and (2) are predicated on the assumption
that environmental effects are no worse than the room
temperature/water inside environment of the fatigue tests.
(4) Branch connections made of materials with val-ues of and sh
that are higher than those for ASTM A106 Grade Bare not necessarily
better in low cycle fatigue strength than A106 Grade B; hence, the
margins indicated in (1) may be re-duced.
(5) ANSI B31.3 uses a margin of 3 on ultimate ten-sile strength
(UTS) in establishing allowable stresses, Sc and Sh. The ASME Code
and B31.1 use a margin of 4. For some materials/tempera-tures; this
means that the margins in (1) would be decreased by a factor of
3/4.
(6) For temperatures in the creep range, allowable stresses
decrease because Sh in Eq. (39) de-creases. However, it is not
apparent that this decrease reflects the actual decrease in low
cycle fatigue strength at temperatures involving creep-fatigue.
(7) The above observations are based on the hy-pothesis that
only cyclic moments included in theSE evaluation cause fatigue
failures. Equa-tion (39) provides some allowance for cyclic
pressures through the term S,, but none for cy-clic thermal
gradients. Fatigue failures due to vibration of small piping
sometimes occur but vibration is seldom included in routine Code
evaluations of s.
4.9 Flexibility Factors In discussing the calculation of S E and
the accuracy
of i-factors, we have been making an implicit assump-tion that
the moments shown in Fig. 3, which come from a piping system
analysis, are accurate. However, present Code guidance for
flexibility of branch con-nections can be very inaccurate. If the
Code guidance is followed, there can be inaccuracies in the
calculated moments and, thus, in S E, that may be greater than that
due to any of the inaccuracies in i-factors we have discussed.
Table 1 shows flexibility factors, k, of "1" for all branch
connections. We do not know what this means and no one that we have
talked to does know. Many people interpret k = 1 to mean that the
juncture of the line representing the run pipe with the line
represent-ing the branch pipe is to be considered as rigid. In the
preceding paragraph, where we indicated that the Code guidance can
be very inaccurate, we are referring
to the rigid-juncture interpretation of the Code guid-ance.
For 1 piping, the ASME Code some guid ance for flexibility of
branch connection with r/R ~ 0.5, R/T ~ 50. This is shown herein as
Fig. 15. This provides a definition of k's that can be readily used
in piping system analysis computer programs. It should be noted
that these k's have a lower bound of zero; hence, footnote 1 in
Table 1 is not applicable.
The significance of k depends upon the specifics of the piping
system. Qualitatively, if k is small com-pared to the length (in
d-units) of the piping system, including the effect of elbows and
their k-factors, then the inclusion of k for branch connections
will have only minor effects on the calculated moments. Conversely,
of course, if k is large compared to the piping system length, then
inclusion of k for branch connections will have major effects. The
largest effect will be to greatly reduce the magnitude of the
calculated moments act-ing on the branch connection.
To illustrate the potential significance of k's for branch
connections, we use the equation in Fig. 15 to calculate k for Mx3
( = Mob) for a branch connection with Do= 30 in., d0 = 12.75 in., T
= t = tn = 0.375 in.:
kob = 0.1(80)1.5(0.425) 112 X 1.00 = 46.6 Reference 28 includes
examples of the effect of branch connection k's on calculated
moments in the piping system shown to scale in Fig. 15. In this
particular example, using the rigid -joint interpretation that k =
1 rather than k = 46.6 leads to overestimating Mob by a factor of
about 9!
Of course, this example was selected to illustrate a rather
extreme k-effect. In most piping systems, the effect would be much
less than a factor of 9. Neverthe-less, it illustrates our main
point; we do not necessarily achieve greater accuracy in Code
evaluations by using more accurate i-factors unless more accurate
k-factors are also used.
The example used above can be continued to illus-trate what is
wrong with using inaccurate k's. Refer-ence 28 happened to
calculate moments for the piping system shown in Fig. 15 for a
temperature increase from 76 F to 500 F, carbon steel material.
Fork = 0 (essentially equivalent to the rigid-juncture
interpre-tation of Code guidance), the calculated Mob is 368,000
in.-lb. The value of SE is then:
SE = i(M/Zb) = [0.9/(T/R)21:l]M/Zb = 10.4(368,000/45.1) = 84.9
ksi
This is well above the Code allowable stress Sx for carbon steel
(e.g., A106 Grade B, for which Sx = 37.5 ksi at most). However, if
the piping system analysis had been done using the more accurate k
= 47, then
S E = 84.9/9 = 9.4 ksi,
and the branch connection is Code-acceptable because SE <
Sx.
Let us follow the designer who believes that the
Stress Intensification Factors 29
-
ND-3686.5 Branch Connections [n Straight Pipe. (Foi branch
connections in straight pipe meeting the dimensional limitations of
NB-3338.) The load dis-placement relationships may be obtained by
modeling the branch connections in the piping system analysis
(NB-3672) as shown in (a) through ~d) below. (See Fig.
ND-3686.5-1.)
(a) The values of k are given below. ForMx3:
k ,.. 0.1 (D IT, )U[(T, It" )(dID))"" (T'6 /T,) For Mz3:'
k ... 0.2(D!T,)l(T,It.)(d!D)J"" (T'6 /T,) where
M=Mx3or Mzl as defined in NB-3683.l(d) D= run pipe outside
diameter, in. d=branch pipe outside diameter, in. lb=moment of
inertia of branch pipe, in! (to be
calc:;ulated using d and T' b) E=modulus of elasticity, psi
T,=run pipe wall thickness, in. 4> =rotation in direction of
moment, rad
(b) For branch connections per Fig. NB-3643.3(a)-1 sketches (a)
and (b):
r. r. if Lt > 0.5[(2r1 + T6 )T.J"" T' if L1 < 0.5[(2r1 +
T6 r ~
{c) For branch connections per Fig. NB-3643.3(a)-l sketch
(c):
t,. ""T' + (-l)y if 0 s 30 deg. T' + 0.385L1 if 0 > 30
deg.
{d) For branch connections per Fig. NB-3643.3(a)-1 sketch
(d):
.f,T',.=T,
Element of negligible length with local flexibility for Mx3 and
Mz3 such that cf> ecron the element Is equal to kMdl1.
Rigid juncture
FIG. NB-3686.5-1 BRANCH CONNECTIONS IN STRAIGHT PIPE
;---.r' 24011 1
}-
ri'" - /,on x 0.375" !'
12.7511 X 0. 37511 I I
J) 12011 -__ -:,
Example: See text _:t
\ '"
Fig. 15-Fiexibility factors, definitions and equations from ASME
Code for Class 1 piping, and example
Code guidance is good and that k = 1 for branch means: assume a
rigid juncture. He is faced with the dilemma of changing the piping
system in Fig. 15 so it does meet the Code. He might consider
changing the piping such as sketched in dashed lines in Fig. 15.
This would be very expensive, so the designer might look at the
possibility of using a pad reinforcement. By using a pad thickness
of 1.5T, he can reduce the SIF to 4.14; his calculated S E is then
33.8 ksi and this might meet Code Sx limits. Let us suppose that it
does and ask what the designer has accomplished by using a pad.
First, since this piping system is assumed to go up to a
temperature of 500 F, the pad may cause high ther-mal gradient
stresses in the 30 in. pipe and thereby reduce its reliability. Has
he improved the fatigue
strength for the cyclic moment, Mob? We do not know much about
the flexibility of a pad
reinforced branch but, since a pad is usually welded to the run
pipe at its inner and outer peripheries, the flexibility might be
estimated by using the equation in Fig. 15 for Mob, but using 2.5T
instead ofT. This would give a flexibility factor of:
kp (for M0 b) e=: 46.6/(2.5)2 = 7 .5. Now, from Ref. 28 data,
fork of 8, it appears that the
moments would be overestimated by a factor of around 3 rather
than a factor of 9 for k = 47. This means that the pad would cause
the moments to in-crease by a factor of about 9/3 = 3. Assuming
that the i-factors for UFT and pad reinforced branch indicate
30 WRC Bulletin 329
-
at least their relative fatigue strength then the UFT to pad
ratio is 10.4/4.14 = 2.5. However, since the mo-ment increased by a
factor of 3, the addition of the pad has decreased the fatigue
resistance of the branch connection.
4.10 The Mob Inconsistency In the preceding, we have attempted
to describe the
complexity of trying to evaluate the fatigue strength of
reducing outlet branch connections subjected to nine moment
loadings. Hopefully, that attempt serves to bring the Mob
inconsistency into perspective.
Looking at Figs. (6), (7) and (8), it would appear that there is
no Mob inconsistency. But instead the Code i-factor equations do
not reflect the complex relation-ship between r/R and stresses. The
remaining ques-tion is: Do fatigue tests reflect the trends shown
in Figs. (6), (7) and (8)?
To answer that question direclty, we would need a series of
fatigue tests on, for example, UFT's with r/R the only variable. We
do not have any such series of fatigue tests. In their absence, we
must assume a para-metric relationship between ir and what we guess
to be the significant parameters; e.g., R/T r/T and r/rp.
Table 13 summarizes relevant fatigue test data; rel-evant
meaning a series of tests including r/R == 1.00 and one or more
tests with r/R less than 1.00. The data is plotted in Fig. 16.
Looking first at UFT's in Fig. 16, we note that prior
to the WFI tests, we had one point on the r/R-curve; i.e.,
Markl's test included in Table 2. Combining this with the WFI
tests, using the parameter (R/T)21:l (t/ T), gives the 3 points
shown in Fig. 16. These show directly that the Code i = 0.9(R/T)
2/:l for OFT's is unconservative for r/R = 0.8 and suggests that
there is a peak somewhere in the range of r/R between 0.5 and
1.0.
The Extruded outlets from Table 6 indicate a possi-ble peak at
around r/R = 0.5. To remind us of the limits of our knowledge, we
have also shown Extruded outlets from Table 3.
The remaining points in Fig. 16 are for branch con-nections
which we think are intended to be covered by Table 1, sketch (f).
It can be seen that the B31.3 Code equation, i =
[0.9/(3.3)21:J](R/T)21:l is unconservative for every point except
the 4 x 4 sizes tests.
One of the main initiators of the Mob inconsistency was the
comparison between the 12 x 6 and 4 x 4 sizes in Table 13, Group D.
The 6 x 4 point in Group D is inconsistent with theory which, as
indicated in Figs. (6), (7) and (8), indicate a peak at r/R
""0.7.
First, comparing Groups D and E, it shoud be noted that Group E
specimens were fabricated by different welders and test as-welded
with a deliberate intent to represent typical field conditions.
Differences in weld details could fully explain the differences
shown in Fig. 16. However, the 8 x 8 size in Group E appears
anomalous in comparison to what would be expected
Table 13. Datu Lcscd for Fig .16; all for M0 b
Fig. 16 Nominal if Type iden. and r/R R/T t/T r/rp . a size l.f
group iden. (R/T) 2/3(t/T)
UFT 8 X 6 0.764 12.9 0.870 0.958 5.84 1.22 A 12 X 10 0.839 16.5
0.973 0.966 8.34 2 1. 32
4 X 4 1.00 8.99 l. 00 0.947 2. 71 2 0.63
Extruded X 16 X 4 0.285 7.26 0.230 0.947 1. 235 l. 42 Table 6 B
8 X 4 0.537 5.50 0.330 0.947 1.484 1.44
6 X 4 0.703 5.39 0.422 0.947 1. 6 53 l. 27 4 X 4 0.943 4.71
0.494 0.947 1.49 4 1.07
Extruded X' 20 X 6 0.326 9.5 0.432 0.935 1.2 0.62 Table 3 c 20 X
12 0.635 9.5 0.687 0.946 2.5 0.81
Weld on {:, 12 X 6 0.513 16.5 0.747 O.G75 3.786 0.78 Table 3 D 6
X 4 0.672 11.3 0.846 0.627 2.203 0.52
4 X 4 1. 00 8.99 1. 00 o. 71 1. 69 7 0.39
Weld on 0 8 X 3 0.396 12.9 o. 671 o. 773 3.20 2 0.87 Table 5 E 8
X 4 0.513 12.9 0.736 0.812 3.49 2 0.86
8 X 5 0.639 12.9 0.801 0.801 4.2o2 0.95 8 X 6 0.764 12.9 0.870
0.832 4. 73 3 0.99 8 X 8 1. 00 12.9 1. 00 0.852 5.19 3 0.94
asuperscript is number of fatigue tests if more than one.
Stress Intensification Factors 31
-
1,
o. A e UFT B I( Extruded, Table 6 C 1(1 Extruded, Table 3
- D A lleld on, Table 3 E 0 \leld on, Table 5
B
Fig. 16-Relevant data on the Mob inconsistency
from theory or from other fatigue tests. We would have expected
the 8 x 8 size ir/[(R/T)213(t/T)] to be around 0.5.
In any event, the available data indicates that the B31.3
equation in Table l(f) is significantly unconser-vative for
reducing outlet Weld Ons and may be un-conservative even for full
outlet Weld Ons. However, the unconservatism appears to be by a
factor of not more than about two. In relation to other
inaccuracies we have mentioned (e.g., use of rigid-joint
flexibility assumption and the B31.3 use of i = 1.00 for torsional
moments), the unconservatism of a factor of two is not particularly
significant.
5.0 Recommendations and Summary Considering the complexity of
the branch connec-
tion problem and the sparsity of information for most parts of
the problem, the Codes have done a good job of providing simple
design guidance. However, as ad-ditional information becomes
available, such as that abstracted in this report, the Code
committees may wish to review and perhaps revise their design
guid-ance to more accurately reflect present information. To assist
Code committees in such a review and possi-ble revisions, we have
prepared a series of recommen-dations. These are listed in what we
consider to be an appropriate order of priority. These
recommenda-tions, in effect, summarize the contents of this
report.
5.1 General Recommendations (1) The ASME Code (Class 2/3), B:n.J
and B31.3
should delete the meaningless "1" in the column headed
"Flexibility Factor, k" for branch connec-tions or tees. A note
should be added, tied to branch connections/tees, such as;
"In piping system analyses, it may be assumed that the
flexibility is represented by a rigid joint at the branch-to-run
center lines juncture. However, the Code user should be aware that
this assumption can be inaccurate and should consider the use of a
more appropriate flexibil-ity representation."
(See discussion in Section 4.9) (2) The ASME Code (Class 2/3)
and B31.1 should
add a note to indicate that "Branch connection" is an acceptable
alternative for unreinforced fab-ricated tees with r/R ~ 0.5; or
delete the descrip-tion of unreinforced fabricated tees. [See
discus-sion in Section 4.6 and Recommendation (10d).]
(3) B31.1 should correct the i-factors for "Branch connection"
to be the same as in the ASME Code (Class 2/3), including the
footnote in (2) above. [See also Recommendation (10).]
(4) B31.3 should include i-factors for "Branch con-nection" to
be the same as in the ASME Code (Class 2/3), including the footnote
of (2) above. (The main purpose of this is to provide realistic
guidance for evaluating the runs of branch con-nections, see
discussion in Section 4.4.)
(5) B31.3 should, in some manner, eliminate the-in-dication that
i = 1.0 for torsional moments ap-plied to branch connections. One
way to do this would be to adopt the resultant moment, single
i-factor approach of ASME and B31.1. However, this would introduce
significant over-conserva-tism for small r/R. An alternative which
might be used is:
(6)
(a) Revise B31.3 Eq. (17) to SE = [S~ + (itS/)] 112
(b) Revise definition of S 1 to: 81 = MJZx
(c) Define i1 as:
Footnote 1, i ~ 1.0, is applicable
(40)
(41)
(42)
(d) Define Zx as Zb for checking branch end, Zr for checking run
ends.
This could introduce some underestimates, but these would be
much less than using the present i = 1.00 and generally would be
more accurate. (See discussion in Section 4.3.) B31.3 should
consider deleting the use of ii = (0.75i0 + 0.25) for branch
connections/tees; i.e., change to show the same factor as is
presently done in (f) of Table 1. The main reason for this
32 WRC Bulletin 329
-
suggestion is for evaluating run ends, where B31.3 gives the
wrong relative magnitude for Mur versus Mir Also it underestimates
the difference between Mob and Mb for r/R between about 0.3 and
0.95 and perhaps over-estimates the differ-ence for r/R below 0.2
and for r/R = 1.0 [See discussion in Section 4.4 and Recommendation
(12).]
(7) B31.1 and B31.3: Add a restriction to the Code i-factor
tables that indicates they are valid for R!T
~ 50. (See discussion in 4.2.1 on validity of R/T
extrapolations.)
(8) All Three Codes: Add a note for branch connec-tions saying
that i-factors are based on tests and/ or theories in which the
branch connection is in straight pipe with about two or more
diameters of run pipe on each side of the branch. The effect of
closely spaced branch connections may require special
consideration. This represents the cau-tion now in footnote 6(c);
see Table 1 herein. Also see Recommendation (10), in which the
footnote is shortened.
(9) All Three Codes: Add a note for branch connec-tions/tees
saying that i-factors are only applica-ble where the axis of the
branch pipe is normal to within 5 of the surface of the run pipe.
This represents footnote 6(b); see Table 1 herein. The i-factors do
not cover laterals or hillside branch connections.
(10) Changes in the present ASME Code, Subsection NC, for
"Branch connection." This recommenda-tion consists of four
interrelated portions. They are presented here and then discussed
in Section 5.2.
(lOa) Change the stress intensification factor equa-tions to: ib
= 1.5(R/T)213(r/R) 112(r/rp);
ib(t/T) ~ 1.5 for (r/R) ~ 0.9, ( 43) ib = 0.9(R/T) 213(r/r
p);
ib(t/T) ~ 1.0 for (r/R) = 1.0, (44) ir = 0.8 (R/T) 213(r/R); 2.1
minimum (45)
where lb = is to be used for checking the branch end and
linear interpolation is to be used for (r/R) be-tween 0.9 and
1.0;
ir = is to be used for checking the run ends. (lOb) Change
footnote (6), in its entirety, to:
"If a radius r 2 is provided that is not less than the larger of
Tb/2, (t~ + Y)/2 [Fig. NC-3673-2(b)-2 sketch (c)] or Tr/2, then the
calculated values of ib and ir may be divided by 2.0 but with ib ~
1.5 and ir ~ 1.5. (Terminology is that of the ASME Code.)
(lOc) Change those portions of the Codes dealing with reduced
outlets to say "For checking branch ends, use Z = 1rr2t and
i(t/
T) in place of i with i(t/T) ~ 1.0." (lOd) Delete the
"Unreinforced fabricated tee" from
Code Fig. NC-3673.2(b)-L (11) Recommendations in (10) are deemed
to be
equally applicable to ASME Code Subsection ND (Class 3 piping)
and to ANSI B31.1
(12) Changes to B31.~3 Analogous to Recommendation (10)
Recommendation (5) would bring the B31 treatment of torsional
moments into better ac-cord with available data and also preserve
the B31.3 approach of keeping separate i's for M0 , Mi and M1
Recommendation (6) suggested deletion of ii = (0.75 ip + 0.25)
because it is incorrect for evaluating run moments.
In keeping with the B31.3 approach, consider-ation might be
given to a set of six SIFs: iob, iib, itb, ior iir and tr The
fatigue test data indicate that iib can be significantly less than
iob and B31.3 may wish to incorporate that difference into their
SIFs.
Figs. 9 and 10, in conjunction with available Mib tests,
suggests'the equation
iib = 0.6(R/T)213 [1 + 0.5(r/R)3](r/rp), but not greater than
iob (46)
For branch connections with r2 provided, use iib/2.
Table 14 summarizes available Mib fatigue test data, previously
given in Tables 2, 3, and 5. Cal-culated values of iib(t!T) by Eq.
(46) are shown. Calculated values of ib(t/T) are also shown so that
the advantage in using separate iob and iib can be seen for the
test models. In general, for r/R between about 0.5 and 0.9, iib ~
0.6 iob At r/R = 1.0 and for r/R < 0.16, iib = iob These iobliib
ratios agree reasonably well with data directly from fa-tigue tests
where both ir for Mob and M;b are available. But the ratios are
less than might be inferred by comparing Fig. 6 and Fig. 9.
If B31.3 were to follow Recommendation (10), then Table l(c) and
(f) should be removed; i.e., Eqs. (43)-(46) are intended to apply
to both UFT's and Weld Ons.
(13) In Fig. NC/ND-3683 2(b)-2 of the ASME Code, delete the
note:
"If L1 equals or exceeds 0.5 vrr:rb then r ~ can be taken as the
radius to the center of Tb." (See discussion at end of Section
4.1.)
Detailed implementation of the above recommen-dations would
require considerable additional work. Nomenclature and consistency
with existing Code text would vary with each specific Code.
Appendix A is a detailed implementation of the recommendations
spe-cifically for NC-3600 of ASME Code Section III. Anal-ogous
changes for ND-3600 would be appropriate. 5.2 Discussion of
Recommendation (10)
No change is intended for ir. We have simply rewrit-
Stress I ntensi[ication Factors 33
-
Table 14. Mib comparisons, fatigue test and Eq. (46)
Source 1i b t/T table Hodel R/T r/R t/T r/rp if i ib t /T ib t/T
number (a) f (b)
UFT 2 4 X 4 8.99 1. 00 l.OO 0.947 2.34 3.68 1. 57 3.68 2 4 X 4
10.6 1.00 1.00 0.955 2.95 4. 15 1.41 4.15 2 4 X 4 22.0 1. 00 1. 00
0.978 6.12 6.91 1.13 6. 91 2 4 X 4 41.8 1. 00 l.OO 0.988 11.0 10.7
0.97 10.7 3 6 X 6 12.0 1.00 1. 00 0.960 3.62 4.53 l. 25 4.53 3 20 X
4 41.4 0. 19 7 1.00 0.942 2.67 6.79 2.54 7. 51 3 20 X 8 24.6 0.375
0.50 0.974 2. 7 5 2.54 o. 92 3.78 3 20 X 14 24.6 0.702 0.60 0.983
3.47 3.51 1. 01 6.27 3 20 X 20 41.4 1.00 l.Oa 0.988 6.90 10.6 1.54
10.6 5 8 X 6 12.9 a.764 a.87a a.958 l. 85 3.36 I. 82 6.01
Weld On 3 4 X 4 8.99 1. oa 1. oa o. 6 3 1.75 2.45 1.40 2. 45 3 4
X 4 8.99 1. 00 1. 00 0.79 1.!36 3.07 1.65 3.07 3 12 X 6 16.5 0.513
o. 7 4 7 0.675 1.28 2.09 1.64 3.51 3 8 X 4 12.9 0.513 a. 7 36 0.79
0.81 2.05 2.53 3.44
Insert 3 14 X 6 18.2 0.466 0.747 0.83 0.98 1. 35 1. 38 2.20 3 12
X 8 16.5 a. 6 71 a.859 a.82 1.52 l. 58 1.04 2.80 3 8 X 4 12.9 a.513
a.736 o. 775 1. oa 1.00 1.aa 1.69 5 12 X 6 16.5 a.513 a.747 0.86a
1.32 1. 33 1. at 2.24 5 12 X 8 16.5 o. 6 71 0.859 a.82a 1.31 1. 58
1. 21 2.80 5 12 X 8 16.5 0.671 a.859 a.874 1.53 1.68 1.10 2.99
(a) Calculated by Eq. ( 46); Inserts have rz provided. (b)
Calculated by Eqs. ( 43) or (44); Inserts have rz provided.
ten the equation to cover the probably more common case of
r2-not-provided. Equations (43) for ib does not have the (t/T)
factor but that is not really a change because of (lOc). Note in
this respect that the present rather complex instructions for
reducing outlets leads to exactly the same SEas our recommended
note: "For checking branch ends, use i(t/T) in place as i and Z =
Zb." By taking the (t/T) out of Eq. (43), this instruc-tion applied
to all branch connections/tees.
The change in the equation for ib is intended to: (a) Provide a
single ib, conceptually the maximum of
i0 b, i;b, i1b, for use with the resultant branch mo-ment. This
is a continuation of present practice, but the ASME might wish to
consider adopting the B31.3 concept of different i-factors; see
Rec-ommendation (12).
(b) Provide an ib that covers the relatively high i-factors for
Mob in the r/R range between about 0.5 and 1.0.
(c) Reduce the over-conservatism in ib to the extent
deemed prudent from available fatigue test data. Table 15
summarizes available Mob fatigue test
data, previously given in Tables 2, 3 and 5. Calculated values
of ib(t/T) by Eqs. (43) or (44) are shown. The right-most column
shows the ratio of i6(t/T)/ir. Con-sidering the scatter encountered
in fatigue tests, we consider the correlation to be adequate. In
particular, the proposed ib adequately solves the Mob
inconsisten-cy. Note that the 8 x 6 and 12 x 10 UFT's are
encom-passed by ib, and the 12 x 6 Weld On is brought into
reasonable consistency with the 4 x 4 Weld Ons. Also note that an
appropriate credit is given for an outer fillet radius, rz; i.e.,
for the 20 x 6 and 20 x 12 Extruded outlets and all Inserts.
While ib provides a good fit to the fatigue test data, it seems
to pose an anomaly with respect to calculated stresses. Assuming
that (R/T) 213 is an accurate param-eter, then the ib equation (for
r/rp = 1) appears as shown in Fig. 8. If Kzb =La, then we would
expect it to be below the theoretical curve by a factor of 2.0.
But
34 WRC Bulletin 329
-
Table 15. Mob comparisons, fatigue test and Eqs. (43) or
(44)
Source ib t/T ib t/T table Hodel R/T r/R t/T r/rp if number (a)
f
UFT 2 4 X 4 8.99 1.00 1.00 0.947 2.71 3.68 1. 36 3 20 X 12 9.5
0.635 0.687 0.946 3.9 3.48 0.89 5 8 X 6 12.89 0.764 0.870 0.958
5.84 6.01 1. 03 5 12 X 10 16.5 0.839 0.973 0.966 8.34 8.37 1.00
Weld On 3 4 X 4 8.99 1.00 1.00 0.63 1. 65 2.45 1. 49 3 4 X 4
8.99 1.00 1.00 0.79 1. 72 3.07 1. 79 3 6 X 4 11.33 0.672 0.846 0.63
2.20 3.31 1.50 3 6 X 4 11.33 0.672 0.846 0.63 1. 87 3.31 1.77 3 12
X 6 16.5 0.513 0.747 0.675 3.78 3.51 0.93 5 8 X 3 12.89 0.396 0.671
0.773 3.20 2.69 0.84 5 8 X 4 12.89 0.513 0.736 0.812 3.49 3.53 1.02
5 8 X 4 12.89 0.513 0.736 0.853 3.45 3.71 1. 07 5 8 X 5 12.89 0.639
0.801 0.801 4.20 4.23 1.01 5 8 X 6 12.89 0.764 0.870 0.832 4.73
5.22 1.10 5 8 X 6 12.89 0.764 0.870 0.868 3.95 5.44 1.38 5 8 X 8
12.89 1.00 1.00 0.852 5.19 4.22 0.81
Extruded 6 4 X 4 4.71 0.943 0.494 0.947 1.49 1. 60 1.07 6 6 X 4
5.39 0.703 0.422 0.947 1.65 1. 55 0.94 6 8 X 4 5.50 0.539 0.330
0.947 1.48 1.sob 1.01 6 16 X 4 7.26 0.285 0.230 0.947 1.23 1. sob
1. 22 3 20 X 6 9.5 0.326 0.432 0.935 1.2 1.50b,c 1. 25 3 20 X 12
9.5 0.635 0.687 0.946 2.5 1. 74c 0.70
Insertc
3 14 X 6 18.2 0.466 0.747 0.83 2.64 2.20 0.83 3 12 X 8 16.5 o.
671 0.859 0.82 2.18 2.80 1.29 3 8 X 4 12.9 0.513 0.736 0.775 1.89
1.69 0.89 5 12 X 6 16.5 0.513 0.747 0.819 2.25 2.13 0.95 5 12 X 6
16.5 0.513 0.747 0.860 2.44 2.24 0.92 5 12 X 8 16.5 0.671 0.859
0.820 2.75 2.80 1.02 5 12 X 8 16.5 0.671 0.859 0.800 2.25 2.74 1.22
5 12 X 8 16.5 0.671 0.859 0.874 2.41 2.99 1. 24
(a) Calculated by Eqs. (43) or (44) as modified by
recommendations (lOb) and (lOc); linear interpolation on 4 x 4
Extruded.
(b) == lower bound of 1. 5. (c) = r2 provided.
Stress Intensification Factors 35
