Proceedings of the ASME 2015 Pressure Vessels and Piping Conference

PVP2015
July 19-23, 2015, Boston, Massachusetts, USA

PVP2015-4

STRESS INTENSIFICATION FACTOR FOR LARGE DIAMETER WELDING TEE

CONNECTIONS

Sadjad Ranjbaran Akbar Daneshvar Ghalelar

Sazeh Consultants Engineering & Construction Nargan Engineers & Constructors
Tehran, Tehran, Iran Tehran, Tehran, Iran
s.ranjbaran@sazeh.co.ir a.daneshvar@nargan.com

ABSTRACT Mo Out-plane moment N.mm

Mt Torsional moment N.mm
Stress Intensification Factors (SIFs) are factors relating to Pl Local Primary Membrane Stress, Mpa
fatigue characteristics of piping components. SIF is fatigue Pl+Pb Primary Membrane Plus Primary Bending Stress,
correlation which compares fatigue life of a typical piping Mpa
component such as a tee and elbow to the reference fatigue life, Pl+Pb+Q Secondary Stress , Mpa
that is girth butt welds in straight pipe subjected to bending Pl+Pb+Q+F Peak Stress, Mpa
moments. In order to calculate localized stress of such piping r Mean Radius of Matching Pipe, mm
component, above mentioned figured out SIF shall be Rx Magnitude of corner radius of shoulder at branch
multiplied by nominal stress. ASME B31 contains several (Crotch radius)
formulas for stress intensification factors considering limitation Sa Axial stress, Mpa
that those formulas are valid only for D/T”100 (diameter to Sb Bending stress, Mpa
thickness). Extending the valid range mentioned in ASME B31 SE Computed Displacement Stress Range, Mpa
this paper is dedicated to SIF calculation for D/T”100 and also St Torsional stress, Mpa
for D/T>100 by utilizing Finite Element Analyzing (FEA) for T Nominal Wall Thickness of Tee, mm
welding tee. The computed SIF for D/T>100 welding tee can T Run pipe Thickness, mm
now be placed to typical pipe stressing program which analyzes Z Section modulus, mm³
piping system using beam elements. In addition, this paper
investigates the effect of Rx (the magnitude of corner radius of
shoulder at branch) on SIF of Welding Tee Connections. INTRODUCTION

There are some mechanisms of piping failure that must be

regarded in the stress analysis of piping systems. These
NOMENCLATURE comprise, but are not limited to:
Bursting due to pressure, Collapse due to dead weight loads,
Ap Cross-Sectional Area of Pipe, mm2 Fatigue due to thermal cycling and Corrosion.
C Distance from the centerline of the branch to the The thermal cycling typically was due to daily start up and
tee-header, mm shut down of a plant. According to ASME piping code B31.3
d Mean branch diameter, mm [1], the typical plant life was 20 years; for this reason the plant
D Mean run pipe diameter, mm was designed for approximately 7000 cycles.
ia Axial SIF
ii In-plane SIF General piping stress softwares use beam theory to model
io Out-plane SIF the mechanical behavior of a piping system. These calculate
it Torsional SIF displacements, forces and section bending stresses directly but
Mi In-plane moment, N.mm the peak local stresses that occur in elbows and tees that caused

1 Copyright © 2015 by ASME

by thermal cycling must be calculated indirectly. The 1955
version of B31.1 introduced this analysis method. The peak [(݅௜ ‫ܯ‬௜ )ଶ + (݅௢ ‫ܯ‬௢ )ଶ ]ଵΤଶ
stress in piping components is calculated by the use of stress ܵ௕ = (2)
ܼ௜
intensification factors. Considering the fact that given SIF
definition in abstract is appropriate for SIF numerical B31.3 combines the bending stress with the torsional and
calculation, the following definition uses for SIF experimental axial stress using:
calculation: stress intensification factor is the ratio of the
elastically predicted stress producing fatigue failure in a given 1
number of cycles in a butt weld on a straight pipe to that ܵா =((|Sa |+Sb )2 +4St2 )2 (3)
producing fatigue failure in the same number of cycles in the
component or joint under consideration. Where the torsional stress and axial stress are given by:
ASME piping codes present empirical formulas for this
factor. These formulas are based on experimental findings by S୲ = i୲ M୲ Τ2Z୧ (4)
A.R.C. Markl and his team in the 1950s [3]. The recent exact
experiments [4] show that Markl’s girth butt weld fatigue curve Sୟ = iୟ Fୟ ΤA୮
should not be used as a basis for SIF calculations of piping
components without an adjustment. Markl’s mean butt weld Where Mi and Mo are the in-plane and out-of-plane moments
curve causes dependency of SIF to low cycle and high cycle for the branch and the two run locations. Whereas in B31.3,
life. This dependency on cycles to failure can be reduced by ii=0.75*io+0.25 and it and ia have a default value of 1.
utilizing the proposed girth weld curve. According to ASME piping codes, it is apparent that
Although piping codes present formula for determination there are shortcomings in the current calculation methods of
of SIF, a recently written code, ASME B31J [5], offers a SIFs for tees which are as follows: [7, 8, 9, 10, 11]:
experimental method for determination of SIF. This may be a -There are no differences between SIFs of reducing tees and
viable method for nonstandard piping fitting. equal tees.
-The SIFs are applied to the run pipe those are equal to SIFs of
the branch pipe
SIFS OF TEES -There is no separate SIF for torsional moments.
ASME has awarded a project to align the stress
Tee connections are among the most complex of piping intensification and flexibility factors of run and branch in in-
fitting to stress analysis. The piping codes ASME B31.3[1], plane out plane and torsional direction in the various B31
B31.1[2] and ASME Section III (for Class 2 or Class 3 piping) piping code via the ASME ST-LLC 07-02 Project [10, 11].
[6] include variety of tee types including welding tees, Nonlinear regression was used to produce correlation equations
reinforced fabricated tees, unreinforced fabricated tees, tees from the FEA result for piping component such as welding tee,
with reinforced branches such as weldolets, extruded outlets reinforced and unreinforced tee, Extruded outlet, Welded-in
and welded-in contour inserts. contour insert, Integrally Reinforced Forged Branch Outlet
ASME Section III (for Class 2 or Class 3 piping) [6] and ANSI Fittings with range of validity: 0.1<d/D<1, 8<D/T<100 ,
B31.1 [2] use similar approaches for analyzing branch 0.3<t/T<3.
connections. In this approach, the branch and each run end are All above mentioned literatures are restricted to a diameter
evaluated, and this methodology results in the calculation of a over thickness (D/T) ratio lower than 100. There are some
stress by the use of the following general expression: studies that break though this restriction which are as follows.
In WRC Bulletin 497 2004 [12], a comprehensive
i(Mi2 +Mo2 +Mt2 )1Τ2 parametric study of large diameter ratio cylindrical shell
SE = (1) intersections subjected to internal pressure and external
Zi
loadings was carried out. This work was extended to calculation
Where Mi , Mo and Mt are, respectively, the in-plane, out-of- of the in-plane and out-of-plane flexibility factors and stress
plane, and torsional moment acting on the branch or run end. intensity factors ZLWKWKHUDQJHRI”G'””'7”
The branch and each of the run ends are evaluated separately. G'”W7”IRUXQUHLQIRUFHG fabricated tees [13]. The effect of
The value of Zi corresponds to the branch or run, depending on geometric parameters on flexibility factors has been also
which is being evaluated. investigated.
The value of i as specified by Section III and B31.1 is the Another study [14] has been carried out on SIF of reinforced
maximum of ii, io, or it where these are the corresponding SIFs fabricated tee using Finite Element Analysis (FEA) for both
to the in-plane, out-of-plane, and torsional moment loading at D/T < 100 and D/T•100.
the point of interest (branch or run point). FE/Pipe which is developed by Paulin Research Group is
In B31.3 [1], bending stresses are calculated at the three points: suitable software to study the pipe component and piping
the branch end and at the two ends of the run pipe. The below system from stress point of view using FEA. In Welding Tee
equation is used to determine these bending stresses: (Shells) module of the FE/Pipe, welding connection can be

2 Copyright © 2015 by ASME

simulated with all geometry parameters. It is able to provide
axial, in-plane, out-plane and pressure SIFs [15].
According to PMS (Piping Material Specification) 6#$.'
documents of refinery or petrochemical projects for some '37#.6'')'1/'64;
services like flare the type of tee connection of large diameter D T Rx-Min Rx-Max
piping must be welding tee. In this paper an attempt will be D/T
(inch) (mm) (mm) (mm)
made to compute SIF for welding tee (normal intersection)
using Finite Element Analysis (FEA) for both D/T < 100 and 50 12.7 100 158.75 242.775
D/T•100.
All geometry parameters of welding tee such as corner 54 12.7 108 171.45 250.825
radius of shoulder at branch, thickness at base, center and top of 58 12.7 116 184.15 269.875
crotch in all direction have effect on stress intensification
factor. In this paper, the effect of Rx (the magnitude of corner 64 12.7 128 203.2 304.8
radius of shoulder at branch) on SIF of welding tee connections 72 12.7 144 228.6 323.75
is only investigated.
80 12.7 160 254 356.25
84 12.7 168 266.7 375
FEA STUDY
88 12.7 176 279.4 387.5
To investigate SIFs of 90 degree equal welding tees, a 90 12.7 180 285.75 393.75
parametric FEA study was carried out for a range of D/T ratios
and minimum and maximum range for crotch radius. The
assumed Minimum [1] and maximum [15] crotch radius is 6#$.'
determined using the following formulas. &+(('4'064Z1('37#.6''
D T Rx
ܴ௫ (‫ܦ = )݊݅ܯ‬ൗ8 (݉݉) (5) D/T
(inch) (mm) (mm)

ܴ௫ (‫ܥ = )ݔܽܯ‬ൗ4 (݉݉) (6) 64 12.7 128 203.20

64 12.7 128 223.52
The maximum Rx taken from WFI tees [15], where C is the
distance from the centerline of the branch to the tee-header pipe 64 12.7 128 243.84
weld. The following table shows the parameters and values for 64 12.7 128 264.16
the FEA model. In this table, D is pipe diameter, T is pipe
thickness, D/T is ratios, Rx (min) and Rx (Max) is respectively 64 12.7 128 284.48
minimum and maximum assumed crotch radius. 64 12.7 128 304.80
In this paper, models based on the parameters of Table 1
were performed. The FEA simulations are performed for all of
them and SIF’s are provided. Table 2 shows different values of
the crotch radius for 64” equal tee from assumed minimum to
maximum Rx in order to study the effect of Rx on SIF.
Finite element analyses were executed with COSMOS
software. Fig.1 shows a typical boundary condition which is
applied to all cases. As mentioned in ASME B31.3 [1] the
piping fitting that not covered in Table D300, we can refer to
ASME B31J [5]. This boundary conditions in Fig.1 are
followed the pattern that is introduced in ASME B31J [5]. In
the model as shown in the Fig.1, in order to calculate the SIF of
branch, in-plane and out-plane loads apply to branch and in the
same way to gain the SIF of header, in-plane and out-plane
loads apply to header. In both cases one end of header must be
fixed.
The length of the run pipe was chosen to be 5 pipe diameters
long and the length of the branch pipe to be 5 pipe diameters
away from center line of the run pipe in order to avoid end
effects [13]. (+)*'#&'4#0&$4#0%*$170&#4;%10&+6+105

3 Copyright © 2015 by ASME

 The FEA mesh model was constructed out using 4 node The shell element represents secondary stress across the
Shell elements with mesh refinement in the intersection region. thickness, that is Pl+Pb+Q. However, SIF represents index for
Fig. 2 shows the typical finite element mesh. fatigue strength that means peak stress, Pl+Pb+Q+F must be
Large diameter welding tee inevitable has weld line. But considered. Normally, the peak stress is the product of the
modeling of this weld line does not have serious impact on the secondary stress and a fatigue strength reduction factor (FSRF)
computed stresses and hence, welds are not part of the model [16]. For instance:
[14].
For checking the isotropy of a finite element model, ܲ௟ + ܲ௕ + ܳ + ‫ܲ( = ܨ‬௟ + ܲ௕ + ܳ) × ‫ܨܴܵܨ‬ൗ2 (8)[17]
percentage change in stress is considered from a model with
very fine mesh to moderately cruder models. Stresses at Gauss According to results the maximum stress location is far
points are checked for integrity of result. For convergence, from the welding line. Therefore, the FSRF is 1 and negligible.
monotonous behavior is checked with a maximum permissible
variation in stress 5%. RESULTS AND DISCUSSIONS

Modeling based on Table 1, for different pipe diameters,

and the constant thickness are carried out. Figures 3 to 6
indicates the mesh and the maximum stress area in the 64”
equal Tee with a minimum crotch radius.

(+)(+0+6''.'/'06/1&'.9+6*/'5*

On the header and branch pipe, element size has been kept as
less than 0.5ξRT at and close to intersection with aspect ratio
less than 2.5, where R is the shell mean radius and T is the shell
thickness [12].
As mentioned earlier, SIF can be defined as the ratio of peak
stress in tee to that in a straight butt welded pipe:

‫ ݐ݊݁݉݋ܯ ݋ݐ ݁ݑ݀ ݏݏ݁ݎݐܵ ݇ܽ݁ܲ ݈ܽݑݐܿܣ‬, ‫ܯ‬

ܵ‫= ܨܫ‬ (7)
2 × ൫‫ܯ‬ൗܼ൯ (+)+0Ä2.#0'*'#&'4´¶4:
/+0
ܲ௟ + ܲ௕ + ܳ + ‫ܨ‬ 
ܵ‫= ܨܫ‬
‫ܯ‬ൗ
ܼ

The factor of 2 is based on the assumption that standard girth

butt welds have SIF between 1.7 and 2.0. The upper value is
used for more conservative [15].

4 Copyright © 2015 by ASME

 
(+)176Ä2.#0'*'#&'4´¶4Z
/+0 (+)176Ä2.#0'$4#0%*Ä4Z
/+0


According to these figures, it is obvious that when load is

applied on header, the value of stress for in-plane direction is
more than out-plane direction. Since the type of loading is
bending, effective area at the intersection has great impact on
value of stress in different direction. The effective area of
bending for in-plane direction is less than out-plane direction.
Therefore, stress value of in-plane direction is more than out-
plane direction.
When SIF of branch is investigated and load is applied on
branch, loading type of in-plane direction is bending. However,
the loading type of out-plane direction is a combination of
bending and torsion. The combination of loads leads to greater
values of stress for out-plane direction. Moreover, the
maximum stress happens at the intersection of welding tee for
all four abovementioned loading types.
The value of SIF for header and branch are presented in
Table 3 and 4, respectively. In each table the SIFs for assumed
minimum and maximum crotch radius can be compared.
Almost the SIF of maximum crotch radius is less than the SIF
of minimum crotch radius. Similar to other literature [14] , the
out-plane SIF value of branch is very high in comparison with
the other SIF.
(+)+0Ä2.#0'$4#0%*Ä4Z
/+0



5 Copyright © 2015 by ASME

 6#$.' a positive relation between header diameter size and the in-
*'#&'4+0Ä2.#0'#0&176Ä2.#0'5+(5 plane and out-plane SIF.
Size In-Plane Out-Plane 
(Inch) Rx (Min) Rx (Max) Rx (Min) Rx (Max) 6#$.'
ґ+0Ä2.#0'176Ä2.#0'5+(5
50 7.37 7.53 5.01 4.49
Header SIF Branch SIF
54 8.45 7.60 5.66 4.55 Rx
58 9.41 10.39 6.11 5.89 (mm) In-Plane Out-Plane In-Plane Out-Plane
64 10.17 10.01 6.77 6.20
203.20 11.32 7.01 16.87 33.67
72 11.63 11.59 7.65 7.15
223.52 11.59 7.39 16.12 32.16
80 12.52 12.54 8.71 6.55
243.84 11.38 6.73 15.75 28.80
84 13.71 12.97 8.77 7.05
264.16 10.42 6.33 15.80 27.92
88 14.03 12.90 8.74 7.57 284.48 10.67 6.49 17.53 28.66
90 14.99 11.65 8.89 7.89 304.80 11.19 6.63 16.24 29.06
6#$.'
$4#0%*+0Ä2.#0'#0&176Ä2.#0'5+(5
Size In-Plane Out-Plane
(Inch) Rx (Min) Rx (Max) Rx (Min) Rx (Max)
30
50 10.71 11.21 20.50 19.53 Header In-Plane
54 11.65 10.38 23.54 18.80 25
58 12.64 14.54 26.28 24.62 Header Out-Plane
64 16.01 14.36 32.77 26.34 20
SIF

72 19.35 18.01 35.94 33.64 Branch In-Plane

80 19.87 17.23 42.16 29.69 15

Branch Out-Plane
84 20.16 18.47 41.40 36.09
88 21.29 18.07 43.81 36.98 10
90 21.96 18.88 45.01 36.77
5
150 200 250 300 350
Rx (mm)
Table 5 indicates the out-plane and in-plane SIFs of the

header and branch of 64” equal welding tee for Rx(Min) to (+)5+(51('37#.9'.&+0)
Rx(Max) with five equal interval. According to Table 5, Fig.7 6''614Z
presents the trends of SIFs of 64” equal welding tee versus Rx.
SIF curves of 64” equal welding tee versus Rx have a
14 B31.3 Out-Plane
minimum. This minimum value occurs in Rx§PPIRU´
equal welding tee. Because the lower value of SIF the better 12 B31.3 In-Plane
condition of piping stress analysis, the above mentioned
minimum value can be considered optimum value. 10 Out-Plane
(Numerical Result)
Fig. 8 shows four curves of SIFs versus pipe diameter. Two
SIF

8 In-Plane
curves are related to SIF below formula of ASME B31.3 [1] (Numerical Result)
table D300 for welding tee. Apparently, this curve is valid for 6
D/T”100. The other curves are numerical result of D/T•100.
4
0.9 2
݅௢ = ଶ
(9)
ܶ ଷ 0 10 20 30 40 50 60 70 80 90 100
ቀ3.1 ቁ
‫ݎ‬ Pipe Diameter (in)

3 1 (+)9'.&+0)6''+0Ä2.#0'#0&1762.#0'5+(1(07
݅ ௜ = ݅௢ +
4 4 /'4+%#.4'57.6#0&$=?8'45752+2'&+#/'6'4

According to Fig.8 the trend of numerical results are

consistent with SIF of ASME piping code formulas which show

6 Copyright © 2015 by ASME

CONCLUSION Determining Stress Intensification Factors (i-Factors) for
The purpose of this paper is to extend the valid range Metallic Piping Components”, The American Society of
mentioned in ASME B31 of welding tee SIF. This paper is Mechanical Engineers, New York, N.Y.
dedicated to SIF calculation for D/T•100 by utilizing Finite 6. ASME Boiler and Pressure Vessel Code, Section III,
Element Analyzing (FEA).The computed SIF for D/T>100 2010, Power Plant Components, American Society of
welding tee can now be used to typical pipe stressing program Mechanical Engineers, New York, NY.
which analyzes piping system using beam elements. In
7. Wais E, Rodabaugh E.C., 2005, “Background of SIFs and
addition, this paper investigates the effect of Rx (the magnitude
Stress Indices for Moment Loadings of Piping
of corner radius of shoulder at branch) on SIF of welding tee
Components”, EPRI Technical Report 1012078.
connections. The general conclusions are as follows:
8. Wais E., Rodabaugh E.C., 1998, “Stress Intensification
- The trend of numerical results consisting with SIF of
Factors and Flexibility Factors for Unreinforced Branch
ASME piping code formulas show a positive relation
Connections”, TR 110996 Final Report, Issued
between header diameter size and the in-plane and out-
November.
plane SIF.
9. Rodabaugh, E.C., 1987, “Accuracy of Stress
- SIF curves of 64” equal welding tee versus Rx have a
Intensification Factors for Branch Connections”, WRC
optimum value.This optimum value of SIFs can be
Bulletin 329, Welding Research Council, New York,
calculated for the other pipe sizes.
N.Y.
- We argue that excessive value of out-plane SIF of
10. Vu P, 2011, “Revision of B31 Code Equations for Stress
branch is due to simultaneous effect of bending and
Intensification Factors and Flexibility Factors for
torsion of out-plane loading on branch of tee.
Intersections”, ECTC Proceedings, Fayetteville, AR.
- It is recommended that torsion and axial SIF of
11. Creates D.H., Côté D.P., 2012, “Alignment of Stress
welding tee with D/T > 100 are studied.
Intensification and Flexibility Factors for The B31 Book
- The vast study must be done on the effect of other
Sections”, PVP2012-78047, Proceedings of the ASME,
geometry parameters of large diameter welding tee
Pressure Vessels & Piping Conference, Toronto, Ontario,
such as thickness at base, center and top of crotch in
Canada.
all direction.
12. Widera, G. E. O., and Wei, Z., 2004, “Large Diameter
- It is suggested that utilizing non-linear regression to
Ratio Shell Intersections, Part 3: Parametric Finite
obtain the formulas for SIF of welding tee with D/T >
Element Analysis of Large Diameter Shell Intersections
100.
_External Loadings_,” WRC Bulletin 497.
13. Xue, L., Widera, G. E. O., Sang, Z., 2006, “Flexibility
Factors for Branch Pipe Connections Subjected to In-
ACKNOWLEDGMENTS Plane and Out-of-Plane Moments”, Journal of Pressure
The authors thank Mr. Fumio Ando of Intergraph, Japan Vessel Technology, Vol. 128 / 89.
for interesting discussions and valuable suggestions and Sazeh 14. Bhattacharya, A., 2011,”A Finite Element-based Study on
Consultants Engineering & Construction Company and Nargan Stress Intensification Factors (SIF) for Reinforced
Engineers & Constructors Company for their supports. Fabricated Tees”. NAFEMS World Congress Boston .
15. Program Manual FE/Pipe Version 5.0, NOZZLE PRO
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