L S. Ong
Nanyang Technological University
School of Mechanical and
Production Engineering,
Nanyang Avenue,
Singapore 2263 Republic of Singapore
Peak Stress and Fatigue
Assessment at the Saddle
Support of a Cylindrical Vessel
The maximum stress in a saddle-supported cylindrical storage vessel is often the
circumferential stress developed at the tips (or horns) of the saddle support. Although
the peak stress at the support is not immediately detrimental to the integrity of a
vessel, it would have a long-term effect on the fatigue life of the vessel. This article
provides a parametric equation to determine the peak circumferential stress at the
support. To assist calculations, a worksheet procedure has been proposed. The parametric equation is accompanied by four graphs, each graph provides values for a
geometric variation of the problem. An example has been shown on the application
of the parametric equation. A fatigue assessment is also made on the example vessel
and comparison is made between ASME and British design codes. The parametric
curves can be also used as a set of design curves for specifying support dimensions.
1
Introduction
Cylindrical pressure vessels are normally supported horizontally by two saddle supports. The main advantage of the twosupport system is that support reactions remain almost the same
should there be an uneven support level due to installation or
relative soil resettlement. For a cylindrical vessel supported by
saddles, the peak stress generally occurs at the top edges (or
horns) of the support, simply due to a structural discontinuity
between the vessel and the support. Over the years, the design
of saddle-supported cylindrical vessel has been based on the
design analysis proposed by Zick (1951), commonly referred
to as the Zick analysis. The analysis was derived on the basis
of ring and beam theories. The beam theory is used to derive
the force and moment distributions along the axis of the cylinder, and the ring theory is used to derive the force and moment
distributions in a cross section. Zick (1951) introduced several
assumptions in his analysis, some of which have no technical
basis, so as to make his theory comparable with the experimental data he had available. The two main assumptions are: (a)
the shear flow distribution in the cross section, and (b) the
effective load bearing areas for direct and bending stresses. In
view of the semi-empirical approach inherent in Zick's analysis,
Tooth et al. (1982) conducted a series of experiments involving
a range of different saddle support configurations; some were
considered rigid and some were flexible. He concluded that
Zick's analysis would provide acceptable results for the force
and stress developed in most parts of the vessel, except in the
support region where the peak stress is sometimes underestimated. In particular, when a rigidly stiffened saddle support
had been used, Zick's analysis would underestimate the actual
peak stress developed in the vessel by a factor of two and
higher.
In view of the semi-empirical approach of Zick's analysis, a
considerable amount of research effort has been directed towards providing a better and accurate solution to the problem. A
few better-known names in this research area are Tooth (1982),
Krupka (1969), Lakis (1978), etc. The present author has also
been involved in the saddle-supported problem for a number of
years and had formulated a general procedure (1988) to allow
for different types of external loads applied on a saddle-supContributed by the Pressure Vessels and Piping Division for publication in the
JOURNAL OF PRESSURE VESSEL TECHNOLOGY . Manuscript received by the PVP
Division, October 16,1993; revised manuscript received January 24,1995. Associate Technical Editor: S. K. Bhandari.
ported vessel. Although it had been verified analytically by
several researchers that the shear force and moment at the support are considerably different from the Zick's analysis, the
Zick design analysis is still currently the recommended design
tool. The fact is that although the method gives a lower peak
stress than the real one, it has rarely caused the vessel to fail
at the saddle support. Apparently, a static reaction load at the
support would hardly cause an immediate failure of the vessel.
The material yield point may be locally exceeded at the peak
stress location; however, the limit plastic state of the cross
section has not been reached and, therefore, no failure would
occur. Although the peak stress at the support is not immediately
detrimental to the integrity of a vessel, it has a direct effect on
the fatigue life of the vessel. Fatigue cracks would develop at
the support due to a highly localized peak stress. For a vessel
which has been in service for many years and for one which
has been subjected to frequent operational fluctuating loading
cycles (of long or short duration), a fatigue assessment of the
vessel may be needed so as to certify its fitness for service
throughout the design life-span or in some cases, beyond the
normal service life-span. In this case, a reliable method for
predicting the peak stress at the saddle support is required. The
next section will present a parametric equation which can be
used to determine the peak stress at the horn of the saddle
support.
2 Parametric Equation for the Evaluation of Peak
Stresses
The theoretical solution to the saddle-supported cylindrical
shell problem is somewhat complex and requires the use of a
computer. Although the theory may give accurate results for any
geometric variation of the problem, it would not be available to
the public. In view of this, a great deal of effort has been made
to express the analytical results for a range of vessel/support
dimensions by means of graphs, tables, and simple equations.
The geometric details of the support, such as the saddle support
angle, width, the wear plate and saddle top plate dimensions,
and its location, are all important factors influencing the magnitude of the peak stress. Therefore, to generate design charts and
data, all these geometric variables must be taken into consideration, especially when the results are intended to be useful to
design.
Tooth and Nash (1991) and the present author (Ong, 1991)
have performed parametric studies for the determination of peak
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stress at the horn of the saddle support. Tooth and Nash (1991)
established a parametric equation with six factors to account
for geometric and physical variations of the problem. Five of
the factors are expressed by a fourth-order polynomial equation;
the coefficients for the polynomials are tabulated for five (r/t)
ratios, ranging from 25 to 250. However, it has to be mentioned
that intermediate values cannot be interpolated from the tables
as they are polynomial coefficients. It is always required to
calculate the two boundary values before a usual interpolation
procedure can be applied. This feature is unfavorable and the
calculation procedure is tedious and time-consuming. On the
other hand, the parametric equation established by the author
(Ong, 1991) is much simpler and involves fewer factors. Moreover, the stress reduction factor due to the use of a wear plate
and extended saddle top plate has been included in the equation.
The parametric study to be presented in this section is a
modified version of the author's previous work (Ong, 1991).
Some of the geometric parameters have been redefined and
some curves have been redrawn in order to cover a wider range
of saddle-vessel dimensions. The cylindrical vessel has a thickness (t), radius ( r ) , and length (L), and the saddle support has
a width (b), a total embracing angle (2/9), and is located at a
distance (a) from one end. The vessel is subjected to applied
loads, such as liquid and self-weight, which generate an upward
reaction force of magnitude ( 2 ) at the support.
The peak circumferential stress at the horn of the saddle
support is expressed by the following parametric equation:
figure. Intermediate values can be found by interpolation. The
geometric ranges in Figs. 1 - 4 will cover more than adequately
all practical vessel and support dimensions. The saddle support
angle can vary between 60 and 180 deg, the saddle width-toshell radius ratio (blr) can vary between 0.1 and 0.5, and the
r/t ratio can vary between 20 and 400.
Factor ks in Eq. (1) is a stress reduction factor, arising from
the use of a wear plate, an extended saddle top plate, or a
flexible saddle support. A wear plate or an extended saddle top
plate, which provides a kind of local reinforcement to the shell
at the support, is an effective way of reducing and moderating
the discontinuity stress developed at the support/vessel junction. Alternatively, a flexible saddle support, which has a gradually reducing sectional stiffness towards the support/vessel
junction, would also reduce the peak stress developed at the
shell junction. Tooth et al. (1982) had shown experimentally
that by using a flexible saddle support, the peak stress developed
at the horn of the saddle can be reduced by as much as 50
percent compared to the use of a rigidly stiffened saddle support.
In the author's view, using a wear plate or an extended saddle
top plate is the most effective and straightforward way of
achieving stress reduction at the support.
Figure 4 provides the stress reduction factor associated with
the extended saddle top plate. The recommended plate extension
is within 3 to 6 deg above the saddle horn; however, the figure
provides values for plate extension up to 12 deg, to cater for a
wider range. It can be concluded from the figure that more than
50 percent stress reduction can be attained with a properly chosen
extended plate or wear plate dimensions. Figure 4 is applicable
®h
Ka* Kb* Kc* Ks* (1)
to saddle support angles ranging from 60 to 150 deg. The insensit2
tivity of the support angle on the stress reduction factor is due
where
to the local character of the peak stress. As the dimensions of
the
extended top plate affect the peak stress significantly, it must
the
peak
circumferential
stress
at
the
support
<?h
be considered in the parametric equation. Otherwise, it will lead
reaction force at the support
Q
to an underestimate of fatigue life of the vessel.
support location factor
K
kb
support width factor
In the case of a rigid support with no extended saddle top
support spacing factor
plate or wear plate, the value of ks is unity. In other cases, k„
a stress reduction factor, associated with the wear plate
Ks
has a value less than one. When a saddle support is built according to a design practice, such as British Standard Institution
or an extended saddle top plate.
BS5276:1983, which provides details for the support construcThe values of these factors can be obtained from Figs. 1 - 4
tion, the support would have a certain amount of built-in flexithrough the following four dimensionless parameters, aa, ab,
bility. A procedure had been suggested by the author (Ong,
ac, and <xs, as defined as follows:
1991) for deriving the stress reduction factor associated with a
few types of saddle support designs. However, the procedure
for ka — Fig. 1, calculate aa = - j (2a)
is not straightforward and the result is only approximate. A
r Vr
more accurate approach is to carry out a finite element study
on different support designs, and subsequently, to obtain a stress
b t
for kb — Fig. 2, calculate ab = - . / (2b) reduction index for each type of saddle support design. As a
rough and first estimate, a saddle support which has a central
web and stiffened by side-plates would give at least a 10-percent
c it
(2c)
for kc — Fig. 3, calculate ac = - , /stress reduction; this value can be adopted here to account for
r Vr
the flexibility of a steel-fabricated saddle support.
for ks — Fig. 4, calculate as = a\L
(2d)
3 Application of the Parametric Equation
The applicable range for each geometric parameter is to be
within the two extreme parametric curves presented in each
A steel vessel (SA516-70) used in a chemical process plant
has the following shell and support dimensions:
Nomenclature
a = distance of support from nearest
end of shell
b = width of saddle support
c = spacing between supports
E = Young's modulus
L = length of cylinder
nt — operational loading cycles
N, = design life cycles
306 / Vol. 117, NOVEMBER 1995
r - mean radius of cylinder
Sa = allowable material design stress
5ait = cyclic stress amplitude
Sr = cyclic stress range
t = shell thickness
U = usage factor (Miner's rule)
a = angular extension of wear plate (or
saddle top plate) above saddle horn
geometric factors in parametric
equation
tr = wear plate thickness
G = support reaction
«<..) = geometric coefficients defined in
Eq. (2)
crh = peak circumferential stress at saddle horn
Transactions of the ASME
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1.1
-
1.0
26= 180c)
\
\ s
-
0.9
a
-
0.8
-
/
r
0.7
0.5
-
0.4
•-•
~~~
26 = Full saddle support angle
•*
/
•'
y
/ /
/ ' /
a
i
\
26 = 60 ° to 120
J
1*
D
!
t
\ :
i.
(_JUUi
Q-
/ /
-
^
. * ' • '
/'
4
0.6
-
• — "
4
26=150 0
-
•
^
i
\
0.3
i
AWS
•
0.2
-
0.1
-
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-• «.-WF
Fig. 1 Support location factor
distance from one end (a) = 1410 mm,
saddle width (b) = 102 mm,
spacing between supports (c) = L — 2a = 4500 mm
length (L) = 7320 mm,
radius (r) = 455 mm,
thickness (t) = 3.3 mm,
8
/
7
26 = Full saddle support angl(*
• 26=60°^
b = support width
,
1':.
^, ._.L_.tk.Lii.
6
5
; 2B=90°^
!
:
V\\\X
\S\SS
4
; 26=120 ° - ^
3
'• 26=150°-^
2
;26=180°—
1
0
0.005
..1...1 - I . - 1
i
11
0.01
i
i-i.
0.02
0.05
0.1
i
i
i i 1 1 1 1
0.2
0.5
Fig. 2 Support width factor
Journal of Pressure Vessel Technology
NOVEMBER 1995, Vol. 1 1 7 / 3 0 7
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1.22
1.20
I
-
-
>
1.14
><
1.12
~
-'*]* J
,
.
i
"
'"•., t
J '*«
I
I
^""^x
1.06
- 90° ,
%
X, N ,
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-
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~%—
*».,
•
-
f\A .ll.ii.--4-.j
2B=- 50
'V,
t
•
-.
9R-Rn
«s.
-
1.08
**^^" • * *
y
•
- 15
1.02
4
**
,
30°
1.10
1.04
I
2(3 = Full saddle support angle
26=90
-
1.18
kc1.16
I
V.
\
2 3=180
N
''V,
V
*
V
v.
*
^
""».. ••».
'•»» '«».,
-
V
- • • « . •^..
^
1.00
^
0.98
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
C
r vr
Fig. 3 Support spacing factor
full support angle (20) = 150 deg.
The specified minimum yield strength for the carbon steel,
SA 516-70, is 38 ksi. The allowable material design stress (Sa)
based on § yield stress would be
Sa
'•Sy = 25.3 ksi (174.55 MPa)
The peak circumferential stress at the horn of the saddle is to
be determined for the case when the vessel is full of water. The
specific weight of water is taken as 9.81 kN/m 3 .
The geometric parameters and their associated factors are
determined according to Eqs. 2(a)-(d)
as follows:
a
It = 0.264,
from Fig. 1: ka = 0.69
ab = -J- = 0.019,
r Vr
from Fig. 2: kb = 1.85
ac = - . - = 0.842,
r \r
from Fig. 3: kc = 1.124
Firstly, assuming that the support is rigid, we obtain as = 0
and k„ = 1.0. The support reaction (Q), due to liquid weight,
is
Q = - Trr2Lp = - (455) 2 (7320)(9.81 • 10' 6 ) = 27,000 TV
The peak circumferential stress at the horn of the saddle can
now be calculated by Eq. (1) as follows:
27000 h 3
ah = (0.69)(1.85)( 1.124)
r J — = 303 MPa
^
'
(3.3)2^455
To facilitate calculation procedure, a worksheet, which is simi308 / Vol. 117, NOVEMBER 1995
lar to that proposed by Tooth and Nash (1991), has been devised to direct the sequence of calculations. The worksheet
also includes all essential information about the vessel and the
support. As an example, to show the use of the worksheet,
the various values and calculations involved in the preceding
example are also reflected in the worksheet in the Appendix.
The calculated value agrees extremely well with the experimental value (302 MPa) reported by Tooth et al. (1982). The
peak stress, according to the Zick design procedure, will be cr/,
= 121 MPa, which underestimates the peak stress by a factor
of 2.5. The Zick design procedure would also tolerate this rigid
saddle support, as it satisfies the allowable stress limit of 1.255„
or 218 MPa. Furthermore, this vessel also satisfies the shakedown criterion in that the peak stress is less than 3 times the
allowable material design stress. However, the experimental
result had clearly shown that Zick's procedure is inadequate for
the rigid saddle support.
The stress developed at the support, according to ASME
Section VIII, Div. 2, may be classified in a conservative manner
as local primary membrane (global and local) plus secondary
bending stress. This stress classification takes into account that
a poorly designed saddle support may produce excessive distortion of the cross section due to a large concentrated support
force. The transfer of load from the support to the shell would
generate a local primary membrane stress and a gross structural
discontinuity would generate a secondary stress. However, in
the Zick design procedure, it is not required to separate the peak
stress into primary and secondary effects. The saddle support
design is deemed satisfactory if the total circumferential stress,
i.e., membrane plus bending, does not exceed 1.25 times the
allowable material stress.
For the vessel used in the preceding example, if the saddle
top plate has an angular extension of 3 deg above the horn of
the saddle and has the same thickness as the shell, the peak
circumferential stress at the support will be reduced by 23 perTransactions of the ASME
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1.2
1.1
Peak stress occurs at the
/ edge of the wear plate
,/
/
Peak stress occurs within
/ the wear plate
J
* 7+
•,
0.9
> \
1
2o*
0.8
t
0.7
3
o
3 0.6
CO
o
0.5
'§
"§
4
5
\
m
j *
*•*
^
•
y \
,.
/'
<
*
*
,/
S '
1*
\ ^ r\
•/ ^
/\
\ 4
V /
V
r\
R
0.4
DC
U
^
\
\
_
—
—
=
=
"^
\
Ar/
_.
<•
•*
• ••
..«""
. . • » " " '
»^^ »^*
s
S
#>
F
l—
.•**
i « ^
l " ^
I B *
-
\l
3
-6
_ ._ — " 9
—
12
-•• » • • 15
_
••
"
0^-bJL
X
0.3
_,„„•
»"•
<
/
7\ \ /
'V
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9 /\ /)
. 0. - n 1
\ t 'J D *< / O.ue
»
i
12
Is 0.02E
15 ""^ i
Xb=0.01 •
X/
angular
extension
60<2B<150 deg.
/^~\
(
\^*\ t ! tr
x
0.2
0.1
0.2
0.4
0.6
0.8
1
V^'*?00^!!t
— 1
k\\SV
1.2
1.4
1.6
sssw
2.2
1.8
2.4
2.6
2.8
1/3
K
s=
K
blV»>
Fig. 4 Stress reduction factor at the wear plate
cent, according to Fig. 4. And if the saddle top plate is extended
to 6 deg above the saddle horn, the stress reduction factor will
be about 0.55. From this example, it shows that by extending
the saddle top plate beyond the saddle horn, the peak stress at
the saddle can be reduced greatly. This method of reducing the
peak stress at the support is definitely more attractive than the
alternative methods, such as making the support construction
more flexible or introducing a soft interface material between
the support and vessel.
4
Fatigue Evaluation
Appendix 5 of ASME Section VIII, Div. 2 (1989) documents
the mandatory requirements for design based on fatigue analysis. Fatigue analysis need not be made if at least one of the
conditions, A or B, stated in Article AD-160.2 of the Code is
satisfied. Condition A requires that the minimum tensile strength
of the material does not exceed 80 ksi and that the number of
expected cycles (due to significant pressure and temperature
variation) does not exceed 1000. Condition B requires that the
maximum number of expected cycles does not exceed the number of cycles given by the applicable fatigue curve of the Appendix, corresponding to an alternating stress of three times the
allowable stress of the material. Both conditions (A and B)
include several other side conditions, all of which must be considered.
The fatigue design curves in the ASME Code were constructed based on fatigue curves obtained from uniaxial strain
cycling data gathered from smooth polished specimens conducted under strain control with zero mean strain and at temperature below the creep range. The design curves have built-in
safety factor of 20 on cycles or 2 on stress, whichever is the
Journal of Pressure Vessel Technology
larger correction, and they have also been adjusted for the maximum effects of nonzero mean stress—as it will give lower
cycles to failure. The fatigue curves are all expressed in terms
of the pseudo-elastic stress amplitude (5 alt ), that is half the
stress range. The data used to derive the design curves were
obtained under strain cycling conditions, and therefore originally expressed in terms of total strain range. These have been
multiplied by an elastic modulus to give a fictitious stress. Although it is not the actual stress in the vessel, it has the advantage of being directly comparable to the stresses calculated on
the assumption of elastic behavior. For this reason, each fatigue
design curve is provided with a value of Young's modulus ( £ ) .
The user of the curve is required to scale the stress amplitude
by a factor (E/E') before using the curve, where E' is the
elastic modulus of user's material.
To use the design fatigue curves provided in the Appendix
5 of ASME Section VIII, Div. 2, the user needs to determine
the largest stress intensity range within a stress cycle at a few
critical points where fatigue evaluation are to be carried out.
For the determination of largest stress intensity range, the Code
gives a step-by-step procedure for two situations: whether the
principal stress changes or does not change in a cycle. The
alternating stress intensity (5an) is then equal to one-half of the
largest stress intensity range. It is to be noted that all stress
values are derived on the assumption of elastic behavior. Once
the alternating stress intensity has been derived and scaled by
the ratio of the modulus of elasticity given on the design fatigue
curve to the value used in the analysis, the number of cycles
can be determined directly from the applicable fatigue curve.
This will be the allowable number of cycles if the operating
cycle being considered is the only one which produces signifi-
NOVEMBER 1995, Vol. 117/309
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cant fluctuating stresses. If there are two or more types of stress
cycles which produce significant stresses, then the alternating
peak stress intensity from each of these cycles will be used to
determine the cumulative fatigue usage factor based on Miner's
damage rule. The structure is considered safe if the summation
of the increments of fatigue damage does not exceed unity. That
is, 2 nIN < 1, where n = no. of cycles at stress a, and N =
allowable no. of cycles from the applicable fatigue curve at the
same stress a.
5 An Example of Fatigue Assessment
In this section, an example of fatigue assessment at the saddle
support will be shown. Two codes' procedures will be compared: ASME Boiler and Pressure Vessel Code (Section VIII,
Division 2, Appendix 5) and British Code BS5500, Enquiry
Case 5500/79.
Statement of the Problem. Suppose that the vessel considered in Section 3 of this article has already been in service for
15 yr, during which it was subjected to daily startup-shutdown
cycles. The chemical contents in the vessel have a specific
weight of 0.63. The vessel had been subjected to a total of 15
hydrotests (once a year), which is required by safety regulation
to certify its fitness for service. The vessel has so far served
the owner well and has now reached the end of its design service
life. It is now proposed to extend the use of this vessel for
another 5 yr; a fatigue assessment is called for.
ASME Section VIII, Division 2, Appendix 5. It has been
known that a welded joint has a much lower fatigue strength
than a smooth polished specimen subject to the same loading
and geometry. It is because locally the weld toe contains cracklike flaws, which are inevitable in fusion welds. For the present
problem, the support is considered to be welded to the vessel
along the edges of the saddle support. Therefore, it would be
inappropriate to carry out fatigue life assessment based on a set
of data generated from smooth polished specimens. Rodabaugh
(1988) carried out a series of fatigue assessment on a range of
pressurized cylinders found that when a factor of 2 is used to
increase the local stress at the weld toe, the results of fatigue
lives agree better with the cyclic pressure fatigue test data. On
the basis that a nozzle-cylinder problem is similar to a supportcylinder problem in terms of local stress behavior, for the present fatigue analysis, the same factor of 2 will be assigned to
the local peak stress at the support.
Using the applicable ASME design fatigue curve for carbon
steel (Fig. 5-110.1 of Appendix 5), the fatigue usage factor U
can be computed as detailed in the following:
stress amplitude for hydrotest (a stress factor of 2 included) =
303MPa(44ksi);
stress amplitude for daily startup and shutdown (a stress factor
of 2 included) = 191 MPa (27.7 ksi);
Young's Modulus = 30 X 106 psi (2.07 GPa).
15 yrs
20 yrs
bears no relation to that of a machined specimen of the parent
material or indeed of a machined butt weld. This is because
fatigue strength of a welded joint depends not only on the weld
geometry, but also on the presence of cracklike flaws at the
weld toe. A fatigue life of a machined component consists of
crack initiation, whereas in a welded component it consists
mainly of crack propagation. As such, results drawn from the
fatigue crack initiation would not be applicable to the fatigue
crack propagation. In Enquiry Case BS5500/79, fatigue data
are provided for different classes (Classes C to G and W) of
weld details. As the fatigue data already incorporate the local
stress concentration factor, they are therefore used in conjunction with nominal stress in the vicinity of the weld.
Besides a graphical presentation of the fatigue design curves,
Enquiry Case BS5500/79 also provides a formula to calculate
fatigue life. The relationship between stress range and fatigue
life is expressed as follows;
S?N = A
In the foregoing, Sr = stress range (expressed in MPa), and A
and m are constants whose values are given in Table 1 of
Enquiry Case 5500/79. Historically, the design S-N curves are
always expressed in terms of stress range (Sr) rather than stress
amplitudes. It may be to emphasize the fact that the full stress
range, tensile or compressive, is the most significant parameter
in fatigue assessment rather than the absolute peak stress, which
is controlled by other stress classification and has its own stress
limit.
To use Eq. (3) in a manner similar to the ASME rule, the
stress range has to be scaled by a factor £72.09 X 105 so as to
cater to other materials with a different Young's modulus. In
addition, if the plate thickness exceeds 22 mm, the stress range
will be reduced by a factor (22/f) 0 ' 25 - This stress reduction
factor is to account for the reduction of fatigue strength in
welded joints as the plate's thickness increases. With these two
correction factors, the fatigue life can be expressed by
N = A
2.09-10 3
m = 3,
(cycles)
(cycles)
(cycles)
hydrotest
44.0
7,000
15
20
25
Filling
27.7
35,000
5475
7300
9125
V = 1n,/N,
0.158
0.211
0.264
By the ASME rule, in view that the fatigue usage factor U is
less than 1, the vessel is therefore safe for a 5-yr extension of
service life.
BS5S00 Enquiry Case 5500/79. Enquiry Case BS5500/
79 of the British Pressure Vessel Code BS5500:1989 acknowledges the fact that the fatigue behavior of a welded structure
(4)
and A = 4.31'x 10"
The preceding values are for the number of total loading cycles
less than 10 7 .
For the hydrotest, Eq. (4) gives Ni = 15053 cycles; for the
daily startup-shutdown of chemical contents, N2 = 60,200 cycles. The load cycles for 15, 20, and 25 yr are the same as
before, and the fatigue usage factors according to BS5500 are
calculated as follows:
25 yrs
(cycles)
310 / Vol. 117, NOVEMBER 1995
Sr
where all stresses are expressed in (MPa) and the term (22/?)
is set to unity when the plate thickness is less than 22 mm.
The fillet weld at the saddle support may be classified as an
F2 weld. From Table 1 of Enquiry Case 5500/79
15 yrs
Hi
(ksi)
(3)
s,
(MPa)
(cycles)
20 yrs
n
Ni
(cycles)
i
(cycles)
25 yrs
n
i
(cycles)
hydrotest
303
15,053
15
20
25
Filling
191
60,200
5475
7300
9125
U = I«,/JV,
0.092
0.123
0.153
The fatigue usage factors for 15, 20, and 25 yr are all well
below 1, so the vessel is again safe in accordance with BS5500
fatigue rule.
For the vessel under consideration, both ASME and BS5500
procedures show that the vessel will be safe for another 5 yr
service. As BS5500 (Enquiry Case BS5500/79) is based on
results obtained from welded joints, it is deemed to be more
Transactions of the ASME
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accurate compared to the fatigue data provided by Appendix 5
of ASME Section VIII, Div. 2.
6
APPENDIX
Determination of Peak Circumferential Stress At the Saddle Support
Concluding Remarks
In a situation where fatigue analysis is required for a vessel
at the support location, Zick's theory would be inappropriate
as it cannot provide an accurate peak stress value at the support.
In this case, the parametric equation presented in this paper
would become useful. In general, fatigue failure is not a problem
for most pressure vessels as the static design procedure has
already built in a fair amount of design conservatism. Fatigue
is rarely a governing criterion of limiting stresses. Nevertheless,
for older vessels and those subject to constant cyclic loadings,
a fatigue assessment may be required. For such cases, the approach described in this article can be followed. It has been
mentioned in this article that the peak stress at the support can
be reduced quite drastically by means of a properly designed
wear plate or extended saddle top plate. The stress reduction
factor associated with the extended saddle top plate can be
determined from the parametric curves provided in the article.
The parametric curves will also be useful to the designer in
specifying vessel and support dimensions.
t r = wear plate thickness
K = angular extension
Vessel Parameters
Saddle Support
Saddle Angle (213) =
Width (b) =
Location (a) =
Support spacing (c) =
Mean Radius (r) = 455 mm
Thickness (t) = 3.3 mm
Length (L) = 7320 mm
150 deg.
102 mm
1410 mm
4500 mm
Wear plate / Extended top plate
Support reaction (self-weight + content)
Q = 27,000 N
V.
IX= 0 (deg)
Factors In the Parametric Equation
References
Location factor
ASME, 1989, Boiler and Pressure Vessel Code, Section VIII, Division 2,
American Society of Mechanical Engineers, New York, NY.
British Standards Institution, 1989, "BS5500: 1989, Unfired Fusion Welded
Pressure Vessels," U.K..
British Standard Institution, 1983, "BS5276:1983, Specification for Saddle
Supports for Horizontal Cylindrical Vessels," U.K..
Lakis, A. A., and Doris, R., 1978, "General Method for Analysing Contact
Stresses on Cylindrical Vessels," International Journal of Solid Structures, Vol.
14, pp. 499-516.
Krupka, V., 1969, "Analysis for Lug or Saddle-Supported Cylindrical Pressure
Vessels," First International Conference on Pressure Vessel Technology, Delft,
The Netherlands, Part 1, pp. 491-500.
Ong, L. S., 1988, "Analysis of Twin Saddle-Supported Vessel Subjected to
Non-symmetric Loadings," International Journal of Pressure Vessels and Piping,
Vol. 35, No. 5, pp. 423-437.
Ong, L. S., 1991, "Parametric study of Peak Circumferential Stress at the
Saddle Support," International Journal of Pressure Vessels and Piping, Vol. 48,
pp. 183-207.
Ong, L. S„ 1992, "Effectiveness of Wear Plate at the Saddle Support," ASME
JOURNAL OF PRESSURE VESSEL TECHNOLOGY, Vol.
114, pp. 12-18.
264
r Jr
Flg(2)
Support width factor
^1 =
Support spacing factor
s
K
B = - ^ = 0.,842
c-rJr
Wear/extended plate factor
Flg(1)
k„= 0.69
0.019
1.85
Flg(3)
kc- 1.124
Fig(4)
k a = 1.0
1 , Or")'
M a x i m u m Circumferential
Stress at the support
Note:
C" n =
k
a -
k
b
-
k
c
k
s f
2
f
=
303 Mpa
1) Numerical data must be consistent In units
2)
" n Is to be reduced by 10% if the saddle horn Is not rigidly stiffened
-
Rodabaugh, E. C , 1988, " A Review of Area Replacement Rules for Pipe
Connections in Pressure Vessels and Piping," WRC Bulletin 335.
Tooth, A. S., Duthie, G. C , White, G. C , and Carmichael, J„ 1982, "Stresses
in Horizontal Storage Vessels—A Comparison of Theory and Experiment," Journal of Strain Analysis, Vol. 17, no. 3, pp. 169-176.
Tooth, A. S., and Nash, A. H., 1991, "Stress Analysis and Fatigue Assessment
of Twin Saddle Supported Pressure Vessels," ASME PVP-Vol. 217, Pressure
Vessels and Components.
Zick, L. P., 1951, "Stresses in Large Horizontal Cylindrical Vessels on Two
Saddle Supports," The Welding Research Supplement, IX, pp. 435-444.
Journal of Pressure Vessel Technology
NOVEMBER 1995, Vol. 117/311
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