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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
.
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ORNL-'p-2472
Conf. 661102-5
A COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS FROM
SPHERICAL SHELLS WITH A SINGLE RADIALLY ATTACHED NOZZLE*
F. J. Witt
R. C. Gwaltney
.
SEP 26 1966
.
CFSTI PRICES
Oak Ridge National Laboratory
Oak Ridge, Tennessee
Oak Ridge, Tennessee
HC. $ 1.00, MN 20

R. L. Maxwell
R. W. Holland
RELEASED FOR ANNOUNCEMENT.
University of Tennessee
Knoxville, Tennessee
IN NUCLEAR SCIENCE ABSTRACTS
Abstract
A series of steel models having single nozzles radially and nonradially
attached to a spherical shell is presently being examined by means of strain
gagos. Parameters being studied are nozzle dimensions, length of internal
nozzle prctrusions, and angles of attachment. The loads are internal pres-
sure, axial thrust, and moment loadings on the nozzle. This paper presents
both experimental and theoretical results from six of the configurations
having radially attached nozzles for which the sphere dimensions are equal
and the outside diameter of the attached nozzle is constant. In some in-
stances the nozzle protrudes through the vessel.
.
1.
*Research sponsored by the U. S. Atomic Energy Commission under con.
tract with the Union Carbide Corporation.
LEGAL NOTICE
Oak Ridge National Laboratory
P. 0. Box Y
Oak Ridge, Tennessee 37831
This report mo prepared us an account of Government sponsored work. Nolter the United
States, por the Commission, por any person souing on behalf of the Commission:
1. Makos any warrupty or representation, oxpropied or implied, with reaprot to the arcu-
racy, completeness, or unofulders of the information container" la the reports or that the use
of way Information, apparatus, method, or proces, daclound lo this refind my rol infringe
printoly owned richto; or
B. Aerumos say liabilities with repoot to the use of, or for demagoa remult, from the
un of aay Information, apparatus, method, or proceda decloud in this report.
As und in the above, person acting og bedall of the Commission" includes may on-
ployee or contractor of the Commission, or omployho of much contractor, to the extent that
such employs or contractor of the Commission, or employee of much controlor preparno,
dienominator, or provides access to, wataformation purmuant to his employment or coatriot
with the Commission, or his omployment with much contructor.
2
:
1
.
9
A
i
2.
Introduction
An experimental test:ing program is being conducted at the University
of Tennessee under subcontract with Oak Ridge National Laboratory. This
work is, in turn, sponsored by USAEC in close cooperation with the Subcom-
mittee on Reinforced Openings and External Loadings of the Design Division
of the Pressure Vessel Research Committee. The program encompasses an
extensive investigation of steel models consisting of a nozzle attached to
a spherical shell and includes the investigation of nonradial as well as
radial attachments. The effects of the nozzle protruding through the veosel
are also being investigated. The loadings of principal interest are internal
pressure, axial thrust on the nozzle, and a bending moment applied to the
nozzle.
Two computer programs have been developed at Oak Ridge National Labo-
ratory by which nozzles radially attached to spherical shells may be :
examined. These are the CERL-II program and the Unified Shell Analyzer.
(USA Code).(2)
The CERL-II code computes the stress distributions in a spherical
vessel and the radially attached nozzie subjected to pressure, and axial
thrust, bending moment and pure shear applied to the nozzle. For the moment
and shear analyses it is assumed that the stresses vary circumferentially
about the junction as the cosine of the circumferential angle measured from
the plane of loading. The nozzle may protrude through the vessel; however,
its junction with the sphere is assumed to be remote from any additional
edge effects. The details of the analysis are given in Reference (3)
*Numbers in parenthesis refer to similarly numbered references in
bibliography at end of paper.
.
in............
.
................
...
.
..
.......
.
The USA code will analyze an ayi symmetric loaded pressure vessel
composed of several difierent types of elemental shell structures,
The
edges of any elemental shell may be close or remote and each shell can
be joined to any logical combination of shell around it. Boundery con-
ditions may be applied to any or all edges. The recent version of the
code accounts for pressure, axial thrust on a riozzle, and thermal loadings,
The theoretical solutions for spherical and cylindrical shells are given
in detail in Reference (4) Both the USA and CERL-JI codes assume the
shells are joined at their middle surface. The codes produce identical
results for duplicate analyses.
The Tirst phase of the testing program at the University of Tennessee
is an investigation of a relatively small nozzle radially attached with
a fixed outside diameter. This phase has now been completed.5) A compari.
son has been made between the experimental data and results from the two
computer programs discussed above. In this paper the more significant
comparisons are presented. Also the variation of experimental stresses
as a function of nozzie protrusion length is discussed as well as the
variation of stresses due to moment loading as a function of the angle
measured from the plane of loading. One example of superposed loadings
is presented.
.
Comparison of Theoretical and Experimental Results
The basic model from which the experimental data were obtained is
shown in Fig. 1. It should be noted that there is essentially no fillet
at the junction. Additional test models were obtained by boring out the
nozzle to a nominal thickness of 0.125 in., cutting off the Internal
-
-
-
.
penetration at two stub lengths; removing the stub altogether, and then
again boring out the nozzle to a nominal thickness of 0.0625 in. The
dimensional and loading data for the six configurations obtained by the
machining processes described above are summarized in Table 1. Each con-
figuration was loaded by an internal pressure, an axial compressive chrust,
and a bending moment applied to the nozzle. One loading on Model I was
a combined pressure and axial compressive thrust load.
A comparison of theoretical and experimental results is shown in
Figs. 2 through 8. The theoreticas results were obtained using' both the
CERL-II and USA codes. Since in these codes the configurations are joined
at the middle surfaces the theoretical nozzle stresses are plotted from that
origin. The experimental data were plotted at distances measured from the
middle surface of the sphere. Gages were located on the inside surface .
of the nozzle at the middle surface of the sphere. The se" data were plotted
at the origin of the nozzle and reflect the sharp gradients thaï exist
inside a junction as shown in photoelastic studies.
. A comparison of theoretical and experimental results for moment, axial
thrust, and pressure loading on Model 1 is shown in Figs. 2 through 4. It
should be noted that the radius at middle surface to thickness ratio for
this model is 4.75 which is outside the thin shell range.®) In Figs. 2 and
3, excellent agreement is found between theory and experiment. No significant
discrepancies are seen to exist for either moment or axial thrust loading.
The comparison for internal pressure is shown in Fig. 4. For this loading
TS
the discrepancies of theoretical and experimental results on the spherical
shell are rather extreme. The meridional outside and circumferential
.
.
.
S
DIWUM
.
inside theoretical stresses fail to possess even the correct curvature.
of the six models tested the results shown in Fig. 4 exhibit the greatest
discrepancy. It is significant that theory and experiment agree quite well
for both the outer and inner nozzles.
:
Similar comparisons for pressure loadings on Models 2, 5, and 6 are
seen in Figs. 5, 6, and 7. Model 2 is similar to Model 1 except the nozzle
has been tored out to a thickness of 0.125 in. Model 5 is like Model 2
except the inner nozzle has been removed. Model 6 is similar to Model 5
except the nozzle has again been bored out and is 0.0625 in, thick. The
agreement between theory and experiment is seen to become progressively
better in these three figures. For the sphere in Fig. 7 the inside cir-
cumferential stresses are in acceptable agreement, Qowever, significant
differences still exist for the outside meridional stresses. The maximum
stresses in the sphere are quite well approximated in Figs. 6 and 7. .
The comparisons for axial compressive thrust on Model 6 are given .
in Fig. 8. Again the results compare quite favorebly. Less agreement is
found for the sphere in the outside meridional stresses than was noted for
the results where the nozzle was thick (see Fig. 3). However, the maximum
stresses in the sphere are better approximated for Model 6. Similar re-
sults exist for moment loading.
Comparisons have been made for all the configurations under all loading
conditions. The results and conclusions are similar to those presented
above.
In particular, the USA code satisfactorily approximated the behavior
as the models were tested with various inner nozzle lengths.
....com.com.co comer ---
............
.........
..
Models 2, 3, 4, and 5 are allke except for the length of Irward
protruding nozzle. The length of protrusions is given in Table 1. Stresses
at points on both the nozzle and the sphere are plotted in Fig. 9 as a
function of inner nozzle length for the three types of loadings. The
locations from which data are presented are not those at which the highest
stresses were found. The locations were chosen on the basis of having com-
plete sets of data for the location. The locations are such, however,
that no change on curvature is indicated between the location in question
and the location of a stress recorded closer to the junction. The curves
are obtained in Fig. 9 by joining the values for inner nozzle lengths of
0, 3/8, 3/4, and 4 1/8 in. and are not drawn consistent with the nozzle approach-
ing a semi-infinite length.
The variations among the three loadings. in Fig. 9 are significant.
For pressure loading there is little effect due to the inner nozzle except
for the outside circumferential stress on the nozzle. This stress which
***
*
is the largest stress at that location on the nozzle increases by over 20%
as the length of the inner nozzle increases, This is in contrast to the
axial load results in which case the larger stresses are changed very little
with the exception of the axial inside stress on the nozzle which shows a
length increases.
In the CERL-II code the stresses are assumed for moment loading to
vary about the junction as the cosine of the angle measured from the plane
*
PAT
ASI
SY
of Loading. Experinental stresses for moment loading were obtained at
: 150 intervals and therefore the validity of the assumption made in the
theoretical analysis may be examined.
The experimental results obtained for moment loading at a given
location on the sphere are plotted at 15° intervals in Fig. 10 for all
six models. Also plotted is o cose where o, is the measured stress in
the plane of loading and @ is the circumferential location about the junction
measured from the plane of loading. Very good agreement is seen to exist
between experimente 1 data. and the assumed variation. Some disagreement
is to be noted for circumierential stresses. Similar agreement exists
for the nozzles
One loading on Model 1 consisted of a combined axial compressive thrust
and internal pressure as shown in Table 1. A comparison of some of these
results and those obtained by superposing results from individual loads
is given in Table 2. Only the comparisons of large stresses are meaning-
ful since experimental error combined with superposing large stresses of
opposite sign can lead to erroneous conclusions. An inspection of the
larger stresses in Table 2 reveal no real trend and indicate that the factors
ignored in the assumption of superposition play no significant role when
the vessel is loaded simultaneously.
Conclusion
The most significant fact obtained from these comparisons is that for
each configuration and all loadings the maximum experimental stresses were
well approximated by the theoretical analyses. This is in spite of the
.......
.
.
fact that for Model 1 the experimental and theoretical stresses on the .
sphere were in considerable disagreement for pressure loading. It is also
significant that in all the models there were no fillets. Thus, stress
concentrations due to the absence of a fillet apparently do not affect
to any great degree the results obtained. It is also worth noting that
for the thinner nozzles the agreement of theory and experiment for the
sphere improves and rather rapidly so for the maximum values under pressure
loading. For these cases (Models 2 through 6) the only significant dis-
agreement is for the meridional outside surface stresses for the sphere
and this disagreement exists for all three loadings considered.
In addition both the CERL-II and USA codes, in general, were
effective in determining the stress distribution in each model for internal
pressure, axial thrust on the nozzle, and a pure bending moment applied
to the nozzle. The stresses around the junction for moment loadings do
vary as the cosine of the circumferential angle with some discrepancies
in the circumferential stresses for the thicker models.
The length of the inner nozzle has very little effect on the stresses
in the sphere and the effect on the outer nozzle depends upon the type of
loading. The greatest effect on the spherical shell stresses come about
were reduced while for axial thrust and moment loads the overall stress
levels were increased. Superposition is seen in general to be valid with
no real trend for the discrepancies obtained.
Bibliography
. "CERL-II – A Computer Program for Analyzing Hemisphere-Nozzle Shells
of Revolution With Axisymmetric and Unsymmetric Loadings," S. E. Moore .
and F. J. Witt, USAEC Report ORNL-3817, Oak Ridge National Laboratory,
October 1965.
"Gas-Cooled Reactor Program Semiannual Progress Report for Period
Ending March 31, 1965," D. B. Trauger and G. D. Whitman, USAEC Report.
ORNL-3807, Oak Ridge National Laboratory, June 1965.
3. "A Critical Study of the Solutions for Asymmetric Bending of Spheri-
cal Shells," F. A. Leckie and R. K. Penny, Welding Research Council
Bulletin No. 90, September 1963.
4. "Analysis of Axisymmetrically Loaded Cylinder-to-Sphere Attachments,"
F. J. Witt and B. L. Greenstreet, USAEC Report ORNL-3755, Oak Ridge
*National Laboratory, April 1965.
"Experimental Stress Analysis of the Attachment Region of Hemispherical
.Sheils With Radially Attached Nozzles," R. L. vexwell, R. W. Holland,
and J. A. Cofer, ME-7-65-1, University of Tennessee Engineering. Experi-
ment Station, Knoxville, Tennessee, June 1965.
6. Thin Shell Theory, V. V. Novozhilov, P. Noordhoff Ltd., Groningen,
The Netherlands, Second Augmented and Revised Edition, 1964, page 2.
.
RT
.
Table 1. Dimensional and Loading Data for the Six Models..
Sphere Redius: 15.254 in.; Sphere Thickness: 0.375 in.; Outside Diameter of Nozzle: 2.625 in.
.
Model
Number
Internal Nozzle
Length
Nozzle
Radiusa
Nozzle
Tickness
Nozzle Radius to
Thickness Ratio
• Loading
Axial Compres-
sive Thrust
(16)
Internal
Fressure
(psi)
-
.
Bending
Moment
(in.-lb) :
4000
8000
6000b
3000
4500
11.25
300
3000
4500
3000
4.125
1.188 0.25
4.75
4.125 1.25 0.125
10.0
300
0.75
.. 0.125
10.0
0.375
1.25
0.125
10.0
300
0.0
1.25
0.125
20.0
300
6
0.0 : 1.281 . . 0.0625
20.5
. 200
"At middle surface.
"Model 1 was also subjected to a simultaneous loading of 400 psi internal pressure
and 6000 lb axial compressive thrust.
4500
4509
.
3000
1500
2400
.
F. J. Witt
- R. C. Gwaltney
R. L. Maxwell
R. W. Holland
Table 2. Superposition of Pressure and Axial Thrust
Loading on a Nozzle Attached to a Spherical Shell
Stresses
Location
Pressure and
Axial Thrust(A)
Pressure(3)
Axial Thrust(C)
B+C
(
(B+C/A)
R. W. Holland
R. L. Maxwell
R. C. Gwaltney
s. vviluu
0.98
5,4°(0)
4,875
14,354
-19,757 -5,403 1.11
5.4°(0)
1,747
17,146
-15,857 1,289 0.74
5.4°(1)
15,653
1,124 · 15,834 16,958 1.08
5.4°(1)
14,176
8,347
6,580 14,927 1.05
5.4°(0)
.-6,076
13,209
-18,867 -5,658 0.93
5.4°(0)
847
15,633
-14,390
1,243 1.47
5.4°(1)
-16,978
2,479
14,186 16,665
5.4°(i).
14,693
8,964
:5,486 14,450 0.98
0.31 in.(0)
-5,703
11,034
-17,459 6,425 1.13
0.31 in.(0) : 1,889
14,080
-12,798 1,282
0.31 in.(1)
1,678
6,762
8,934
2,172
1.29
0.31 in.(1) 5,393
12,462
.-7,220 5,242 0.97
The pressure loading was 400 psi and the axial load was 6000 lb compressive on.
Model 1.
bLocation of nozzles is given in inches from outer surface of sphere; location on
sphere is given in degree from apex; (i) refers to inside surface; (o) refers to outside
surface. The same locations refer to duplicate gages.
CAt a given location, the first stress is an axial or meridional stress and the
second stress is a circumferential stress.
0.68
m
armorgonautovara
mwagowo campeonowe...
10:
Captions
Fig. 1. Cross-Sectional View of Hemisphere and Nozzle Assembly -
Model l.
.
.
Fig. 2. Comparison of Theoretical and Experimental Results in Plane
of Loading on Model 1 for a Pure Moment Loading of 8000 in.-lb
on the Nozzle.
Fig. 3. Comparison of Theoretical and Experimental Results on Model l.
.
.
for an Axial Compressive Thrus': Ioad of 6000 lb on the Nozzle.
· Fig. 4. Comparison of Theoretical and Experimental Results on Model 1
for an Internal Pressure of 400 psi.
Comparison of Teoretical and Experimental Results on Model 2
for en Internal Pressure of 300 psi.
Fig. 6. Comparison of Theoretical and Experimental Results on Model 5
for an Internal Pressure of 300 psi.
Fig. 7. Comparison of Theoretical and Experimental Results on Model 6
. for an Internal Pressure of 200 psi.
Fig. 8. Comparison of Theoretical and Experimental Results on Mudel 6
for an Axial Compressive Ioad of 1500 lb on the Nozzle. .
Stresses (on the right) as a Function of Inner Nozzle Length.
Fig. 19. Variation of Stresses Around the Junction for Moment Loading.
as a Function of the Circumferential Angle Measured: From the
Plane of Loading.
F. J. Witt
R. C. Gwaltney
R. 1. Maxwell
R. W. . Holland.
to present
.
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2.625" 1 0.003"
2.125" - 0.003
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0.3809
1,031" Dia.
(36. Holos)
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Canc 66-4531

(x10
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xx 103

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INNER SURFACE OF WNER NOZZLE
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Fig.
ORAL DWG 64-11295A


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Fig5
ORAL-OVS 66-4881


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ORNL-OWG 65 - 374 IA

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Fig. 8

ORNL-OWG 66.4899

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MERIDONAL OUTSIDE
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(x103)


(x103)
LERIDOVAL INSIDE
CIRCUMFERENTIAL INSIDE
-AXIAL INSIDE
AXIAL THRUST
STRESS (psi)
STRESS (psi)
CIRCUMFERENTIAL –
AINSIDE
CIRCUMFERENTIAL
OUTSIDE
--AXIAL OUTSIDE
MERIDIONAL OUTSIDE -
C'RCUNFERENTIAL OUTSIDE
12 3
4
NOZZLE EXTENSION (in.)
4
5
1 2 3
NOZZLE EXTENSION (in.)


MER:D QIVAL INSIDE
CIRCUMFERENTIAL
INSIDE
AXIAL
KIAL OUTSIDE
:
CIRCU:ZFERENTIAL
OUTSIDE
STRESS (psi)
STRESS (psi)
MOMENT
CIRCUMFERF.NTIAL
INSIDE
.
-
CIRCUMFERENTIAL OUTSIDE
CIRC
2
MERIDIOVAL OUTSIDE
-AXIAL INSIDE
1
.
1 2 3
NOZZLE EXTENSION (in.)
1 2 3 4
NOZZLE EXTENSION (n.)
Fig.
9
Ant
12
With
pogle
ORAL.ONG H-4809
CONFIGURATION 2

CONFIGURATION 1
OUTER SURFACE
OUTER SURFACE


6:02
TER SURFACE
OUTER SURFACE
0
15 30 45 60 75 900
15
30 45 60 75 90
O
15
30 45 60.75
15
30 45
60 75 50
MERIDIONAL STRESS (osi)
CIRCUMFCRENTIAL STRESS (osi)
MERIDIONAL STRESS (PS4)
ARCUVFERENTIAL STRESS (osi)




INNER SURFACE
INNER SURFACE
INNER SURFACE
INNER SURFACE
i
.
0
15
30 45 60 75 So 0 15 30 45 EO
CIRCUMFERENTIAL ANGLE 6 deg)
75 90
O
15 30 45 60 75 90 0 15 30 45.60 75 %
CIRCUMFERENTIAL ANGLE 18 deg!
CONFIGURATION 4
X10%
CONFIGURATION 3
TITO 100 TTT
OUTER SURFACE
OUTER SURFACE




OUTER SURFACE
OUTER SURFACE
-
COS
-
i
TO 15 30 45 60 75 S
O
15 30 45
15
75 90
CIRCUMFERENTIAL STRESS (psi)
30 45 60 75
NERIDIONAL STRESS (osi)
30 45 60 75 90
MERIDIONAL STRESS (psi)
CIRCUMFERENTIAL STRESS (psi)




INTER SURFACE
LIVER SURFACE
WER SURFACE :
WWER SURFACE
O
15
90
O
30 45 60 75 90 0 15 30 45 60 75
CIRCUNFERENTIAL ANGLE 18 dog)
15 30 45 60 75 90 0 15 30 45 60 75
CIRCUMFERENTIAL ANGLE 18 dag)
90
CONFIGURATION 5
CONFIGURATION 6


103,
(x103


OUTER SURFACE
OUTER SURFACE
OUTER SURFACE
OUTER SURFACE
15
30 45 60
75
90
15 30 45 60 75 90
O
15 30 45 60 75 904
O
15 30 45 60 75 90
' MERIDIONAL STRESS (psi)
CIRCUMFERENTIAL STRESS (psi)
MERIDIONAL STRESS (psi)
CIRCUMFERENTIAL STRESS (osi)




INNER SUPS
INNER SURFACE
WNER SURFACE
INNER SURFACE
.
-
•
-
•
0
15
30 45 60 75 90 0 15 30 45 60 75 90
CIRCUMFERENTIAL ANGLE (8 org!
0
15 30 45 60 75 90 0 15 30 45 60
. CIRCUMFERENTIAL ANGLE 19 dro
75 90
tigilo
.
..
-
- -
END
-
-
-
DATE FILMED
10/31 / 66







WS.
72
T
.
.
wil
14LIN
11
17
IL
H
.C.
K
UL