Parametric study of the thin shell solution of internally pressurized spherical vessel–cylindrical nozzle juncture is used to develop simplified closed-form formulas of stress concentration factor (SCF) as functions of the key vessel–nozzle geometric parameters known to influence the solution. The SCF values are not based on the vessel stresses alone; nozzle stresses are also analyzed and the corresponding SCF determined. Therefore, for a given vessel–nozzle juncture, the designer will be left with adequate information upon which to decide the controlling SCF. Predictions by the proposed equations are validated using finite element method (FEM). Consequently, design charts are presented based on both the vessel's and nozzle's SCF as predicted by the proposed expressions.

References

References
1.
Leckie
,
F. A.
,
1961
, “
Localized Loads Applied to Spherical Shells
,”
J. Mech. Eng. Sci.
,
3
(
2
), pp.
111
118
.
2.
Hetényi
,
M.
,
1938
, “
Spherical Shells Subjected to Axial Symmetric Bending
,”
Bull. Int. Assoc. Bridge Struct. Eng.
,
5
, pp.
173
184
.
3.
ASME
,
2004
, ASME Boiler and Pressure Vessel Code (BPVC) Section VIII Division 2,
ASME
,
New York
.
4.
Mukhtar
,
F. M.
, and
Al-Gahtani
,
H. J.
, “
Comprehensive Evaluation of SCF for Spherical Pressure Vessels Intersected by Radial Cylindrical Nozzles
,”
Int. J. Pressure Vessels Piping
(in press).
5.
Attwater
,
I. J. S.
,
Anderson
,
J.
, and
Findlay
,
G. E.
,
1994
, “
Three-Dimensional Finite Element Analysis of Sphere/Cylinder Intersections Under Axisymmetric Loading
,”
Int. J. Pressure Vessels Piping
,
57
(
2
), pp.
231
235
.
6.
Naderan-Tahan
,
K.
,
1995
, “
Stress Concentration Factors in Spherical Vessels With Single Oblique Nozzle
,”
J. Eng., Islamic Repub. Iran
,
8
(
2
), pp.
95
105
.
7.
Dekker
,
C. J.
, and
Brink
,
H. J.
,
2000
, “
Nozzles on Spheres With Outward Weld Area Under Internal Pressure Analyzed by FEM and Thin Shell Theory
,”
Int. J. Pressure Vessels Piping
,
77
(
7
), pp.
399
415
.
8.
Schindler
,
S.
, and
Zeman
,
J. L.
,
2003
, “
Stress Concentration Factors of Nozzle-Sphere Connections
,”
Int. J. Pressure Vessels Piping
,
80
(
2
), pp.
87
95
.
9.
Qadir
,
M.
, and
Redekop
,
D.
,
2008
, “
SCF and Fatigue Analysis of Sphere-Nozzle Intersections With LTA
,”
ASME
Paper No. PVP2008-61176.
10.
Chaudhari
,
S. S.
, and
Jadhav
,
D. N.
,
2012
, “
A Suggested Stress Analysis Procedure for Nozzle to Head Shell Element Model–A Case Study
,”
Int. J. Theor. Appl. Res. Mech. Eng.
,
1
(
2
), pp.
92
98
.
11.
Luo
,
C.
, and
Song
,
S.
,
2012
, “
Finite Element Analysis of Spherical Shell With Opening Nozzle
,”
Inf. Technol. J.
,
11
(
4
), pp.
426
430
.
12.
Al-Gahtani
,
H.
,
Khathlan
,
A.
,
Sunar
,
M.
, and
Naffa'a
,
M.
,
2014
, “
Local Pressure Testing of Spherical Vessels
,”
Int. J. Pressure Vessels Piping
,
114–115
(
1
), pp.
61
68
.
13.
Mackerle
,
J.
,
1997
, “
Finite Elements in the Analysis of Pressure Vessels and Piping–A Bibliography (1976–1996)
,”
Int. J. Pressure Vessels Piping
,
69
(
3
), pp.
279
339
.
14.
Mackerle
,
J.
,
1999
, “
Finite Elements in the Analysis of Pressure Vessels and Piping, an Addendum: A Bibliography (1996–1998)
,”
Int. J. Pressure Vessels Piping
,
76
(
7
), pp.
461
485
.
15.
Mackerle
,
J.
,
2002
, “
Finite Elements in the Analysis of Pressure Vessels and Piping, an Addendum: A Bibliography (1998–2001)
,”
Int. J. Pressure Vessels Piping
,
79
(
1
), pp.
1
26
.
16.
Mackerle
,
J.
,
2005
, “
Finite Elements in the Analysis of Pressure Vessels and Piping, An Addendum: A Bibliography (2001–2004)
,”
Int. J. Pressure Vessels Piping
,
82
(
7
), pp.
571
592
.
17.
Mackerle
,
J.
,
2002
, “
Finite and Boundary Element Linear and Nonlinear Analyses of Shells and Shell-Like Structures: A Bibliography (1999–2001)
,”
Finite Elem. Anal. Des.
,
38
(
8
), pp.
765
782
.
18.
Naghdi
,
A. K.
,
1969
, “
An Approximate Solution to the Problem of a Circular Cylindrical Shell With a Circular Hole Subjected to an Arbitrary Self-Equilibrated Edge Loading
,”
Arch. Appl. Mech.
,
38
(
6
), pp.
380
388
.
19.
de Carvalho
,
E. A.
,
2005
, “
Stress Concentration Factors for an Internally Pressurized Circular Vessel Containing a Radial U-Notch
,”
Int. J. Pressure Vessels Piping
,
82
(
7
), pp.
517
521
.
20.
Lotsberg
,
I.
,
2008
, “
Stress Concentration Factors at Welds in Pipelines and Tanks Subjected to Internal Pressure and Axial Force
,”
Mar. Struct.
,
21
(2–3), pp.
138
159
.
21.
Pilkey
,
W. D.
, and
Pilkey
,
D. F.
,
2008
,
Peterson's Stress Concentration Factors
,
3rd ed.
,
Wiley
,
Hoboken, NJ.
22.
Oliveira
,
S. C.
,
Deus
,
E. P.
, and
Mont'Alverne
,
A. M.
,
2010
, “
Finite Element Analysis of Pipes Considering the Effects of Stress Concentration Factors Due to Dents
,” Sixth Annual Conference on Multiphysics Modeling and Simulation (
COMSOL 2010
), Boston, MA, Oct. 7–9.
23.
Pinheiro
,
B.
,
Pasqualino
,
L.
, and
de Azevedo
,
N.
,
2013
, “
Stress Concentration Factors of Dented Rigid Risers
,”
ASME
Paper No. OMAE2013-10128.
24.
Lind
,
N. C.
,
1965
, “
A Rapid Method to Estimate the Elastic Stress Concentration of a Nozzle in a Spherical Pressure Vessel
,”
Nucl. Struct. Eng.
,
2
(
2
), pp.
159
168
.
25.
Lind
,
N. C.
,
1967
, “
Approximate Stress-Concentration Analysis for Pressurized Branch Pipe Connections
,” ASME Pressure Vessels and Piping: Design and Analysis, Pittsburgh, PA, Nov. 12–17,
ASME
Paper No. 67-WA/PVP-7, pp.
951
958
.
26.
Leckie
,
F. A.
,
Paine
,
D. J.
, and
Penny
,
R. K.
,
1967
, “
Elliptical Discontinuities in Spherical Shells
,”
J. Strain Anal.
,
2
(
1
), pp.
34
42
.
27.
Money
,
H. A.
,
1968
, “
Designing Flush Cylinder-to-Cylinder Intersections to Withstand Pressure
,”
ASME
Paper No. 77-PVP-17.
28.
Decock
,
J.
,
1975
, “
Reinforcement Method of Openings in Cylindrical Pressure Vessels Subjected to Internal Pressure
,”
Weld. Res. Abroad
,
21
(
9
), pp.
9
36
.
29.
Xie
,
D. S.
, and
Lu
,
Y. G.
,
1985
, “
Prediction of Stress Concentration Factors for Cylindrical Pressure Vessels With Nozzles
,”
Int. J. Pressure Vessels Piping
,
21
(
1
), pp.
1
20
.
30.
Moffat
,
D. G.
,
Misty
,
J.
, and
Moore
,
S. E.
,
1999
, “
Effective Stress Factor Correlation Equations for Piping Branch Junctions Under Internal Pressure Loading
,”
ASME J. Pressure Vessel Technol.
,
121
(
2
), pp.
121
126
.
31.
Gurumurthy
,
K.
,
Jain
,
R.
, and
Salpekar
,
V. Y.
,
2001
, “
Simplified Formula for Stress Concentration Factor in Radial Nozzle Shell Junctions Under Internal Pressure Loading
,” ASME Pressure Vessels and Piping Conference, Atlanta, GA, July 22–26, pp.
3
6
,
ASME
Paper No. PVP-430.
32.
Timoshenko
,
S. P.
, and
Woinowsky-Krieger
,
S.
,
1970
,
Theory of Plates and Shells
,
McGraw-Hill
,
New York
.
You do not currently have access to this content.