Int. J. Pres. Ves. & Piping 26 (1986) 145-166
ASME Code Classification of Pipe Stresses:
A Simplified Elastic Procedure
A. K. Dhalla
Westinghouse Electric Corporation, Advanced Energy Systems Division,
Madison, PA, USA
and
G. L. Jones
O'Donnell and Associates, Inc., Pittsburgh, PA, USA
(Received: 8 March, 1986)
A BSTRA CT
Liquid Metal Fast Breeder Reactor (LMFBR) plants utilize thin-walled
components to minimize thermal stresses due to coolant temperature
transients. A non-integral, insulated pipe clamp is generally used to
support high temperature pipes and minimize thermal interaction between
the piping and the support system. The resultant clamp-induced pipe
stresses require consistent classification into primary and secondary stress
categories as defined by the A S M E Code. A simplified stress classification
procedure is proposed in this paper to split the clamp-induced pipe stresses
into primary and secondary categories.
INTRODUCTION
The pressure vessel components and piping systems in a Liquid Metal
Fast Breeder Reactor (LMFBR) plant are considerably thinner than
those designed for the Pressurized Water Reactor (PWR) plant. The
nominal thickness of the PWR structural components is primarily
dictated by the internal pressure loading. In contrast, the internal
145
Int. J. Pres. Ves. & Piping 0308-0161/86/$03.50 © Elsevier Applied Science Publishers
Ltd, England, 1986. Printed in Great Britain
146
A. K. Dhalla, G. L. Jones
pressure in an L M F B R (loop type) plant is considerably smaller than
in a PWR, hence the structural components are designed to be as thin
as possible to minimize thermal effects.
Typically, the nominal radius-to-thickness ratios of these LMFBR
structural components range from 25 to 70, hence they may be
realistically thought of as thin-walled structures. For example, the pipes
considered in the present study are large radius (0.457 m and 0.305 m)
thin-walled (12.7mm) pipes which transport liquid sodium, at elevated
temperatures (546°C-585°C), in the Primary Heat Transport System
(PHTS). The predominant displacement-controlled loading in these
thin-walled piping systems is due to the thermal movements of the
system and the thermal transients postulated for these plants. Thus,
theoretically, to minimize thermal stresses, it is beneficial to reduce the
pipe thicknesses and to design flexible piping loops. However, due to
the interaction between a relatively thin LMFBR pipe and a stiff clamp,
an evaluation is required of the local stresses at pipe supports. However,
in applying the ASME Code t'2 acceptance criteria, it is not clear whether
these local pipe stresses should be considered as primary or secondary.
The purpose of this paper is to present a simplified procedure to
classify local stresses, induced by the piping restraint assembly, into the
primary and the secondary categories designated in the ASME Code. 1.2
The example used to illustrate the simplified stress classification
procedure is that of a pipe clamp structural assembly used in the Clinch
River Breeder Reactor Plant (CRBRP). The simplified method presented
here was originally developed in Ref. 3 and was successfully used in
Ref. 4 to quantify primary stress due to elastic follow-up in the CRBRP
piping system.
In the Fast Flex Test Facility (FFTF) the clamp-induced pipe stresses
were conservatively designated as primary. In the CRBRP the clamp
preloads as well as the hanger and snubber loads are significantly higher
than those in the FFTF. Consequently, it was not possible to assume
the local clamp-induced pipe stresses to be primary and still comply
with ASME Code 1'2 primary stress limits. Additional analyses were
performed to understand and evaluate the pipe response due to preloads
and external loads imposed on the pipe clamp. The two- and threedimensional finite element models to represent the pipe clamp geometry
were presented in earlier papers. 3'5 The local stresses used in this paper
were obtained from a three-dimensional finite element model presented
in Ref. 5.
ASME code classification of pipe stresses
147
TYPICAL PIPING RESTRAINT ASSEMBLY
Figure 1 shows a typical piping restraint assembly used in the CRBRP.
The external loads at the hanger and snubber locations are transmitted
by the pipeline clamps attached to the pipe. The design parameters and
loadings imposed on the piping have dictated specialized design features
for the CRBRP pipe clamps to support long horizontal and vertical
runs of pipe. These aspects of design are discussed in detail in Refs 6
and 7. A brief description of the clamp is as follows.
To minimize the potential for local discontinuity stresses in the liquid
metal piping, a non-integral insulated pipe clamp was designed to serve
as an attachment point for load hangers and seismic restraints. The
clamp is composed of two semicircular bands with bolt flanges, gussets
and attachment lugs welded to the bands, as shown in Fig. 1. In addition
to these metal outer bands, there are two semicircular bands of sheathed
24" PI
CLAM
SNUBBER
Fig. 1. Typical 24in pipe restraint assembly for CRBRP.
148
A. K. Dhalla, G. L. Jones
Fig. 2.
Full three-dimensional clamp/pipe interaction model.
ASME code classification of pipe stresses
149
load-bearing insulation attached to the inner surface of the clamp from
the pipe. The assembly is held in place by bolts and Belleville spring
stackups that are preloaded at assembly. This produces an initial contact
pressure between the clamp assembly and the surface of the pipe.
The Belleville spring stackups are designed to accommodate thermal
expansion of the pipe without introducing large changes in the bolt or
spring loads or the contact pressure at the pipe/clamp interface.
BACKGROUND
Prior work included preparation of two- and three-dimensional finite
element models to examine parametrically different load combinations
and to evaluate pipe/clamp interaction effects. 4'5 The final threedimensional pipe/clamp interaction model used in the present study is
shown in Fig. 2. To reduce computation cost only a quarter model was
used to represent the pipe and the clamp geometry. The two planes of
ATZ=4.211cm
AT Z = 0.0 em
/~
4,400N
/
2,200N~
f
f
CENTER
OFCLAMP
ATZ- 13.2cm
AT Z" 15.2 ¢m
4 , 4 0 0 N ~ 4 , 4 0 0 N
EDGE OF
Fig. 3.
CLAMP
Interface load distribution for 178 000N preload.
A . K . Dhalla, G. L. Jones
150
125
100
75
A
so
E
I--
a.
25
0
0
X
PRELOAD
-25
-50
50
~
A
25
~
ul
,,r
~
BENDING
0
EMBRANE
X
I
-25
0
I
I
50
100
I II
150
200
I
250
300
350
PRELOAD (kN)
Fig. 4.
Pipe wall stress c o m p o n e n t s as a function o f preload with an assumed initial
gap distribution.
ASME code classification of pipe stresses
151
symmetry used in analysis are: (a) a longitudinal plane through the
clamp split line along the length of the pipe, and (b) a transverse plane
through the center of the clamp band. For nonlinear elastic analysis,
the initial gap distribution was based upon the worst case tolerance
stackups between the corresponding maximum/minimum radii of the
pipe O.D., the insulation band I.D./O.D., and the clamp band I.D.
Figure 3 shows the interface loads on the pipe due to the clamp preload
of 178 kN, which is the design preload for this clamp configuration. The
load distribution at different axial locations in the pipe shows that the
interface loads are high under the outer gusset plate at z = 13.2 cm, and
these interface loads decrease away from the gusset. The preloaded bolts
as positioned on the clamp thus impose significant line loads on the thin
circular pipe, which deforms and redistributes the stresses as more gaps
are closed around the circumference and along the length of the pipe.
Interestingly, the maximum stress occurs not at the outer gusset, but at
the clamp center line where the largest pipe deformations are present.
The stresses at the outer gusset are high but not as high as at the center
line. Figure 4 shows the variation of maximum hoop and axial stresses
as the preload is increased. The peak membrane and bending stresses
occur at different preloads, because of the change in interface loads (on
the pipe) due to the change in gap distribution. Thus, from the point
of view of application of the ASME Code it is difficult to classify these
stresses arbitrarily: e.g., the local bending stress as secondary and local
membrane stress as primary. Furthermore, the clamp is subjected to
external loads which may change the gap distribution and, consequently,
the stress distribution at different load levels. Therefore, in the following
sections a simple procedure based upon elastic analyses is presented to
classify clamp-induced stresses (in the pipe) as primary or secondary as
implied philosophically in the ASME Code. The proposed method uses
the CRBRP clamp for illustration, but it does not depend upon any
specific clamp configuration.
CLASSIFICATION OF LOAD-CONTROLLED A N D
D I S P L A C E M E N T - C O N T R O L L E D QUANTITIES
The design of reasonably conservative piping systems requires careful
classification of induced stresses into primary (P) and secondary (Q)
stress categories. The basic characteristic of a primary stress is that it
152
A. K. Dhalla, G. L. Jones
is not self-limiting (see NB-3213.8 of Ref. l). Primary stress is not
redistributed or relieved by inelastic deformation. The structural
response is equilibrium-controlled or load-controlled, hence primary
stresses may be alternatively described as equilibrium-controlled or loadcontrolled stresses. The basic characteristic of a secondary stress is that
it is self-limiting (see NB-3213.9 of Ref. 1). Secondary stress is caused
by displacement constraints and is redistributed or relieved by inelastic
deformation. These inelastic deformations may be in the form of
time-independent plastic strains or time-dependent creep strains. The
structural response is predominantly compatibility-controlled or deformation-controlled, hence secondary stresses may be alternatively
described as compatibility-controlled or deformation-controlled stresses.
Primary stresses which can result in failure from a single application
of load are limited to relatively low allowable values. Secondary stresses
which can result in failure only from repeated load cycles are less
severely limited. It is the range and the number of cycles of secondary
stress (rather than the level of stress) that are of particular importance
in preventing failure by exhaustion of ductility or gross distortion, or
due to creep-fatigue interaction. Thus, the importance attached to the
ASME Code classification of stresses, into primary and secondary
categories, derives from their relationship to modes of failure.
Elastic secant modulus procedure
If the local stress due to pipe/clamp interaction is redistributed then
that stress may be considered secondary. This redistribution may occur
due to material nonlinearity (plasticity and creep) or due to geometric
nonlinearity (gap redistribution). An inelastic analysis would show how
this redistribution proceeds as the clamp preload is increased. Unfortunately, such an inelastic analysis is quite expensive, and it is difficult to
quantify the primary-secondary split even if an inelastic analysis is
performed. Therefore an elastic secant modulus approach, discussed
below, was developed to quantify the primary-secondary split.
The elastic analysis procedure is based on the concept that the local
material flexibility in the plastic (or creep) region can be simulated by
lowering the elastic modulus of the pipe. This is illustrated schematically
in Fig. 5, which shows a plot of the generalized local stress versus the
local strain experienced by a pipe subjected to clamp preload. If the
clamp preload were to produce a purely load-controlled situation, then
153
A S M E code classification of pipe stresses
/
/
!
G9
/
J
/
/
N
!
E1
E2
I
/
Controlled
II'•r•'•---100%
Deformation Controlled
el
E2
Generalized Local Strain
Fig. 5.
Load-controlled and deformation-controlledresponses.
a change in elastic modulus from E 1 t o E 2 would not affect the initial
local stress o-1, but strain would increase from e 1 to e2 as represented
by the horizontal line AB in Fig. 5. On the other hand, if the preload
were primarily a displacement-controlled loading, then the change in
elastic modulus would not affect the initial local strain el, but the initial
local stress would drop from 0"1 to a 2 represented by the vertical line
AC in Fig. 5.
Figure 6 shows the inelastic response predicted by the pipe/clamp
interaction model, s The applied preload is plotted against the local
effective strain, ee, at the most highly loaded location in the pipe. At
loads above 80 kN the material nonlinearity increases significantly with
the increase in load. This inelastic response can also be simulated by
using an elastic secant modulus, E s, for pipe material under the clamp.
Two preload cases (178 kN and 267 kN) were analyzed using appropriate
secant moduli with zero initial gap distribution. The secant modulus
values for these two cases were calculated from the ratio of the effective
154
A. K. Dhalla, G. L. Jones
60
Elastic
/
Analysis-~t/
50
/
/
I
/
Secant - ~ l
Modulus E2 = 88 GPa
I n e l a s t i c ~
Analysis
for
40
Preload = 267 kN
/
/
/
Secant Modulus, E1 = 130 GPa
for Preload = 178 kN
@,
l
30
2O
lo
Elastic Modulus
Eo = 194 GPa
2
4
6
8
10
12
Effective Strain, Ceff (10 .4 in/in)
Fig. 6.
Comparison of inelastic and secant modulus elastic analyses.
stress to the effective strain at the most highly stressed location in the
pipe for the corresponding preload. The effective strains obtained from
the elastic secant modulus analyses are also plotted in Fig. 6. The close
correspondence in this figure between the points obtained from elastic
secant modulus analyses and the curve obtained from inelastic analysis
suggests that the pipe flexibility can be reasonably represented by either
elastic-plastic material properties in inelastic analysis or by reducing
the elastic modulus in an elastic analysis. Of course this simplified
procedure would estimate local responses at the highly loaded locations
reasonably well. At stress levels less than 25% of the maximum stress
the predictions would be unsatisfactory. However, this shortcoming of
the simplified procedure is only of academic interest because to comply
with the ASME Code rules, an analyst generally selects the most highly
loaded locations and ignores the lower stressed regions in the structure.
ASME code classification of pipe stresses
155
The results presented in Fig. 6 were obtained using secant modulus
for pipe material directly under the clamp, and elastic modulus for the
rest of the pipe/clamp assembly. The rationale for this selection is as
follows. At load levels higher than the design preload, redistribution of
local plasticity and/or initial gaps reduce the clamp-induced pipe bending
stresses (Fig. 4), and the interface load distribution becomes more
uniform (Fig. 3). Thus, the basic characteristic of secondary stress is
realized, that is the clamp-induced pipe stresses cannot precipitate failure
in a single load application. Although a detailed sensitivity study to
select the appropriate pipe length for reduced secant modulus was not
performed, a good correlation between detailed inelastic and secant
modulus (elastic) analysis confirms the adequacy of the simplified
procedure proposed in this paper.
In summary, if the local stresses induced in the pipe are purely
deformation-controlled quantities (secondary) then the corresponding
stress ratio (ax/a2) would vary in direct proportion to the material
flexibility ratio (El~E2), and the correspondence strains would be
constant. That is,
a--! =--El
when ~1 = g2
(1)
E2
O"2
On the other hand, if the local stresses are predominantly loadcontrolled, then the corresponding strain ratio would vary inversely
with the material flexibility ratio and the correspondence stresses would
be constant. That is,
e2
~1
-
El
E2
when o l = o-z
(2)
P R E L O A D E D C L A M P - I N D U C E D PIPE STRESSES
In a practical problem, neither eqn (1) nor eqn (2) could be satisfied
based upon the actual numerical values predicted by elastic secant
modulus analyses. The numerical difference between the exact satisfaction of eqns (1) and (2) and the actual stress and strain ratio predictions
would provide a measure of local stress that is considered primary. This
is illustrated in Fig. 7, where normalized equivalent or effective stress
at the outside surface of the clamp is plotted against the normalized
equivalent effective strain. The numerical values are based upon four
156
A. K. Dhalla, G. L. Jones
100% Load-Cont rolled
2
%-
%o
0P u = 30 o. 0P I = 0 o
Upper Bound Percent Primary = 33%
Lower Bound Percent Primary = 0%
~6~
g
Symbol
Modtrtus Ratio
E/El
~8~
Z
(3
1
O
A
2
3
O
10
10 - -
tE
•
!~"--
12
0
(:oe = ee
2I
100% Deformation-Contro,led
4I
6I
8
10
Normalized Equivalent Strain (6ie/foe)
Fig. 7.
Primary-secondary split based upon equivalent elastic analysis for preloaded
case (outside surface).
elastic analyses with E o / E i = 1, 2, 3 and 10. The purpose of performing
more than three elastic analyses is to establish a trend of stress relaxation
with respect to the reduction o f secant modulus.
Figure 7 is a normalized plot so that the portion that can be designated
as primary can be represented by the relative position of the line A D
with respect to the 100% load- and deformation-controlled lines.
The angle 0 p, between the 100% deformation-controlled line AC and
ASME code classification of pipe stresses
157
the equivalent elastic stress-strain response represented by line AD,
measures the deviation from 100% displacement-controlled loading.
For example, if the predicted stress ratio had increased in direct
proportion to the moduli ratio, and if the corresponding strains
remained constant, then 0p would be zero and the primary stress
contribution due to clamp/pipe interaction would be 0%. In contrast,
if 0p were 90 ° then the primary stress contribution would be 100%.
A linear variation may be assumed in between these two extremes. For
example, an upper bound primary stress contribution due to the
pipe/clamp interaction as obtained from Fig. 7 is given by
0p
0-7 x 100 = 33%
(3)
In subsequent discussion, eqn (3) will be used to classify the local clampinduced stresses into primary and secondary categories. Conceptually,
the primary-secondary split based upon elastic secant modulus analyses
is straightforward. However, when numerical values are plotted in Fig.
7, for Eo/E l = 1 to 10, the elastic stress and strain predictions do not
fall on the straight line AD. This nonlinear behavior is due to changes
in gap distribution, which alter the interface loads and the clamp-induced
pipe stresses. As pipe becomes more flexible, the strains remain nearly
constant, and the response plotted in Fig. 7, at E/Ei greater than 3, is
closer to the deformation-controlled line. Thus, if the clamp is overloaded
during faulted condition, the mode of failure will be similar to that due
to the application of a secondary stress as implied in the ASME Code.
In Fig. 7, two values of primary stress split are presented: (a) a
conservative upper bound value defined by the solid line AD, and (b)
a reasonable lower bound value defined by the dotted line AE. The
lower bound value of clamp-induced primary pipe stress is considered
reasonable because (a) it accounts for the stress reduction due to
plasticity and redistribution of interaction loads, and (b) one application
of such clamp-induced stresses would not cause failure in the pipe.
However, in some cases a designer might neglect the stress relief due to
material or geometric (gap redistribution) flexibility offered by the clamp
design and use a conservative upper bound value presented in Fig. 7
for clamp-induced primary pipe stress.
The rationale for limiting the elastic moduli I(E/Ei) ratio to 10 is
presented in Fig. 8. This figure shows the isochronous stress-strain
curves, at t = 0 and t = 200 000 h, for the piping material. The life of
158
A. K. Dhalla, G. L. Jones
24
~
E/E 1 = 1
t
I
20
t =2x105
=
0 hrs.
hrs.-
E/E 2 = 2
,>"//
- E/E 3 = 3
/
/
/
16
I\
/
."
12
I
\
I
/
\
D
t
f
/
/
/
//
/
/
/
/
/
/
/
//
//
//
/'~---
E/E,=,o
/
/
/
/
0
I
I
I
I
]
0.2
0.4
0.6
0.8
1.0
Strain (%)
Fig. 8.
lsochronous stress-strain curves for 316SS piping material.
the CRBR plant is about 200000h, hence the material flexibility
represented by E / E l = 10 corresponds to a strain of about 1%. In a
piping system the pipe/clamp interaction stress is only a part of the total
bending strain experienced by the pipe at the most highly loaded
location. Limiting the total bending strain to 1% due to pipe/clamp
interaction is a reasonable assumption. The inelastic strain limits
specified in Code Case N-47 are 2% for bending and 1% for membrane
A S M E code classification of pipe stresses
159
strains. Therefore, it is sufficient to limit the elastic analyses to E / E l = 10
to obtain reasonable classification of the pipe/clamp interaction stress.
Local stresses for preloaded clamp reevaluated
The example shown in Fig. 7 represents the case of a clamp preloaded
to the maximum design preload. The primary-secondary split illustrated
!
I
I
_ ._A_
~A~,~
B
,~Obn
"
4
g
f~
~
O~u
~
~eb._ ~
D
Symbol
~AIt~
I ~
10
c;
i
2
Component
Membrane
Rending
I
I
I
4
6
8
10
Normalized Strain, % = ~i / ~:o
Bending Component Split
Membrane Component Split
0 PU=370 ,0P1=230
OPm = 90 ° , Percent Primary = 100%
Upper Bound Percent Primary = 41%
Lower Bound Percent Primary = 26%
Fig. 9.
Primary-secondary stress split for membrane and bending stress components
(preload case).
A. K. Dhalla, G. L. Jones
160
in Fig. 7 is based upon the surface stress at the most highly stressed
location at the split line of the pipe (point A in Fig. 2). The surface
stress in ASME Code terminology includes the primary membrane
( e m ) ' primary and secondary bending (Pb and Q), and peak (F) stress
components. Consequently, the primary-secondary stress categorization
at the inside and outside surface would be different if the primarysecondary split were calculated as shown in Fig. 7. For example, Fig. 4
shows that the membrane stress components (at the same split line
location) increase nearly proportionately with the increase in the preload
applied to the clamp. In contrast, the bending stress components increase
up to the design load and then decrease with further increase in preload.
In order to include the interaction of membrane and bending components
and to evaluate their redistribution as the pipe becomes more flexible,
it was necessary to calculate the primary-secondary split separately for
the membrane and the bending stress components.
Figure 9 shows the membrane and the bending stress component
plots, respectively, for the preload case with zero initial gap distribution.
These plots are based upon four elastic analysis results, where the elastic
modulus in the pipe under the clamp is reduced ( E / E i = 1, 2, 3 and 10),
to simulate redistribution of stresses in the inelastic range when the
pipe becomes more flexible. Although the plots at various axial and
circumferential locations in the pipe are not shown, the observed trend
TABLE 1
C l a m p - I n d u c e d Pipe Stresses and Strains due to a Preload o f 40 Kips
(Location: center o f clamp, underneath clamp split line)
Normalized
modulus
Equivalent
stress
(psi)
Equivalent
strain
(in~in)
Normalized
stress
Normalized
strain
Membrane components
1
2
3
10
3500
3980
3840
3 160
1.24
2.84
4.08
11-3
x
×
x
x
10 -4
10 4
10 -4
10 -4
1.0
0.88
0.91
1.11
1.0
2.29
3.29
9.11
4.89x
6.84 x
8.02 x
12.0 x
10 4
10 4
10 -4
10 -4
1.0
1.44
1.82
4.27
1.0
1.40
1.64
2-45
Bending components
I
2
3
10
13760
9580
7540
3220
ASME code classification of pipe stresses
161
is similar to that shown here at the most highly stressed location. The
numerical values presented in Table 1 show that the membrane stresses
are basically primary in nature, because the membrane stresses are
nearly constant for E / E t varying from 1 to 10. In contrast the bending
stresses are predominantly secondary in nature, because they redistribute
as the pipe becomes more flexible. In Fig. 9, the conservative upper
bound clamp-induced primary stress in the pipe may be considered to
be 41%, whereas a more reasonable lower bound primary stress is
considered to be 26%.
E X T E R N A L LOADS A P P L I E D TO P R E L O A D E D C L A M P
Local stresses for externally loaded clamp
When the pipe clamp is connected to a snubber, the clamp would
transmit an external seismic load to the pipe. Without a three-dimensional interaction model (Fig. 2) it is not possible to calculate the local
clamp/pipe interaction stresses during such seismic events. Traditionally,
only the nominal beam stress (Mc/I, where M is the m o m e n t applied
to a pipe of a m o m e n t of inertia, I, and c is the distance of the extreme
fiber from the pipe neutral axis) is calculated and the clamp/pipe
interaction effects are ignored. However, for the thin-walled L M F B R
piping it is necessary to calculate these local interaction stresses to
properly evaluate the primary stress limits specified in the ASME Code.
To reduce the computation costs, a quarter symmetry model (180 °
Sector, Fig. 2) was utilized for symmetric (split line) external load cases.
Two load cases were investigated: (a) vertical tensile external load, and
(b) vertical compressive external load. These load cases are sketched in
Fig. 10, wherein a constant preload was maintained during application
of the external loading. Four elastic analyses with E / E I = l, 2, 3 and
10 were performed for these two load cases. We are interested in the
local membrane and bending stress caused by the pipe/clamp interaction.
These local stresses are in addition to the nominal beam type bending
stresses where the pipe section is assumed to be circular. Thus, the final
primary stress limit checks would include not only the nominal beam
type stresses but also the primary local stresses as calculated by the
equivalent elastic analysis procedure described earlier.
The numerical values tabulated in Tables 2 and 3 are used to arrive
162
A. K. Dhalla, G. L. Jones
q~
Vertical, Compressive (VC)
Vertical, Tensile (VT)
Fig. 10.
External load cases examined.
at the primary-secondary split shown in Fig. 11 for the external load
cases. This figure shows the membrane and the bending stress component
plots for the external vertical tension and vertical compression. Both
these cases include a design preload that would be experienced by this
clamp. The effective stress results separated into membrane and bending
parts show similar trends as those observed earlier for the preload clamp
without external load. Once again, the membrane stresses could be
conservatively considered as primary for the A S M E Code type calculations. At higher load levels, substantial stress redistribution is experienced
by the pipe due to higher material flexibility (E/E~ greater than 3);
and the clamp-induced local bending stresses, shown in Figs 9 and 1 l,
are closer to the deformation-controlled line than to the load-controlled
line. For these external load cases a conservative upper bound local
bending stress may be considered as 56% primary. On the other hand,
a reasonably local bending stress for design may be considered as 41%
A S M E code classification of pipe stresses
163
TABLE 2
C l a m p - I n d u c e d Pipe Stresses a n d Strains Due to a n External Vertical C o m p r e s s i o n
L o a d o f 40 Kips a n d a Preload of 40 Kips
(Location: center o f clamp, u n d e r n e a t h c l a m p split line)
Normalized
modulus
Equivalent
stress
(psi)
Equivalent
strain
(in~in)
Normalized
stress
Normalized
strain
Membrane components
1
2
3
10
4430
3890
3670
3340
1.58
2-78
3.91
11.9
x
x
x
x
10 -4
10 - 4
10 - 4
10 - 4
1-0
1.14
1.21
1.33
1.0
1-76
2-47
7-53
9780
6630
5240
2310
3.48
4.74
5'58
8'25
x
×
x
x
10 - 4
10 - 4
10 - 4
10 - 4
1.0
1.48
1.87
4.23
1-0
1.36
1-60
2.37
Bending components
1
2
3
10
TABLE 3
C l a m p - I n d u c e d Pipe Stresses a n d Strains Due to an External Vertical Tension Load o f
40 Kips a n d a Preload o f 40 Kips
(Location: c e n t e r o f clamp, u n d e r n e a t h clamp split line)
Normalized
modulus
Equivalent
stress
(psi)
Equivalent
strain
(in~in)
Normalized
stress
Normalized
strain
Membrane components
!
2
3
10
7250
6440
5820
4090
2"58
4"59
6-19
14"6
×
x
x
×
10 -4
10 -4
10 - 4
10 -4
1-0
1-13
1"25
1-77
1.0
1.78
2'40
5'66
23 160
17200
14030
6650
8.24
12.3
14.9
23.8
x
x
x
x
10 - 4
10 - 4
10 -4
10 -4
!.0
1-35
1.65
3.48
1.0
1.49
1.81
2-89
Bending components
!
2
3
10
A. K. Dhalla, G. L. Jones
164
m ,,
I
I
I
I
+I
A
bn
ii
c
6
D
Symbol
Component
Load Case
A
Membrane
Vertical Compression
0
Bending
Membrane
[]
10
c
Vertical Tension
Bending
I
I
I
1
2
4
6
8
10
6 n = ~-i/~o
Bending Component Split
Membrane Component Split
0 Co
0~ *
= 500
0 CI
= a?o
,no Percent Primo. = 100~
Upper bound percent primary = 56%
Lower bound percent primary = 41%
F i g . 11.
Primary and secondary stress split for membrane and bending stress components (external load case).
primary as indicated by the dotted line in Fig. 11. These observations
have been confirmed by similar results plotted for various axial and
circumferential locations in the pipe. It should be emphasized that Fig.
l l shows just one of a number of locations investigated in the present
study. Special post-processing programs were written to evaluate the
simplified elastic analysis results. Thus, the upper and lower bound
percent primary stress values shown in Fig. 11 envelop the data generated
ASME code classification of pipe stresses
165
in the present study. Additional conservatism built into the present
recommendation for primary-secondary split is the fact that the highest
pipe stress due to operative mechanical and seismic loading does not
occur at the same location as the highest clamp-induced primary stress.
C O N C L U D I N G REMARKS
Piping restraints or clamps are routinely used to support thermal
expansion loops (piping runs) used in an LMFBR plant. However,
clamp/pipe interaction effects are not analyzed routinely for these thinwalled (25 < r/t < 70) piping systems. A three-dimensional finite element
clamp/pipe interaction model was developed to evaluate the effect of
clamp on pipe. Inelastic as well as nonlinear elastic analyses were
performed to calculate the local stresses induced in the pipe due to
preloading of the clamp. To comply with the ASME Code requirements
it is necessary to classify these clamp-induced local stresses into primary
and secondary categories. Unfortunately, inelastic analysis is expensive
and it cannot be used to quantify the primary-secondary split of the
local stresses induced in the pipe. However, inelastic analysis is useful
in evaluating the deformation response of the pipe to distinguish
qualitatively a load-controlled primary loading from a deformationcontrolled secondary loading.
An elastic secant modulus procedure was developed to classify the
local stresses into primary and secondary categories. This simplified
procedure requires local stress predictions from at least three elastic
secant modulus analyses, with different (more flexible) elastic moduli,
to simulate the material and/or geometric nonlinearity in the clamp/pipe
structural model. The adequacy of this approach was confirmed by
comparing the elastic secant modulus analysis results with those obtained
by a detailed inelastic analysis.
The simplified equivalent elastic procedure does not depend upon the
specific clamp design or the pipe geometry. The classification of stresses
into primary and secondary categories is based upon the ASME
Code definition of the load-controlled and the deformation-controlled
structural response.
The local stresses due to clamp/pipe interaction can be categorized
as follows: (a) the membrane stress components are predominantly
primary; (b) the bending stress components are only 30-50% primary.
166
A. K. Dhalla, G. L. Jones
At loads higher than the design load levels substantial local stress
redistribution is experienced by the pipe due to higher material flexibility
( E / E i greater than 3), and gap redistribution between the clamp and the
pipe.
A C K N O W L E D G E M ENTS
This paper is based on work performed under subcontract to Westinghouse Electric Corporation, Advanced Reactors Division, on US Department o f Energy Contract EY-76-15-2395. The authors wish to express
their appreciation for the technical contributions made by R. M. Mello,
L. P. Pollono and Dr R. H. Mallett.
REFERENCES
1. A S M E Boiler and Pressure Vessel Code, Rules of Construction of Nuclear
Power Plant Components, Section III, Division 1, American Society of
Mechanical Engineers, New York, 1977.
2. A S M E Boiler and Pressure Vessel Code Case N-47 (1592), Class 1 Components in Elevated Temperature Service, Section III, Division 1, American
Society of Mechanical Engineers, New York, 1977.
3. Jones, G. L., An evaluation of clamp effects on LMFBR piping systems, in
Effects of piping restraints on piping integrity, PVP-40, pp. 201 17, American
Society of Mechanical Engineers, New York, 1980.
4. Dhalla, A. K., Verification of an elastic procedure to estimate elastic followup, in Design of elevated temperature piping, PVP-Vol. 86, pp. 81-96,
American Society of Mechanical Engineers, New York, 1984.
5. Jones, G. L. and Dhalla, A. K., Classification of clamp induced stresses in
thin-wailed pipe, ASME paper 81-PVP-I 7, American Society of Mechanical
Engineers, New York, June 1981.
6. Pollono, L. P. and Mello, R. M., Design considerations for CRBRP heat
transport system piping operating at elevated temperatures, ASME paper
79-NE-5, American Society of Mechanical Engineers, New York, 1979.
7. Pollono, L. P. and Mello, R. M., Design and testing of CRBRP insulated
horizontal and vertical pipe clamps, in Effects of piping restraints on piping
integrity, PVP-40, pp. 177-200, American Society of Mechanical Engineers,
New York, 1980.