Background of the Half-Pipe

M. I I . J aw ad
Chief Engineer,
Jacket Rules in Section VIII,
Nooter Corporation,
P.O. Box 451, Division 1
St. Louis, MO 63166
New rules for the design of half-pipe jackets were developed by theASME Subgroup
on Design of Section VIII. This article gives the background information for the
derivation and various assumptions made in developing the rules.

The 1991 Addendum to ASME's Section VIII, Division 1 The bending hoop stress is given by
Code contains a new nonmandatory appendix for the design Shb=U Sb (5)
of half-pipe jackets. The Appendix includes charts as well as
equations for obtaining the allowable jacket pressure on the and the total hoop stress is
shell and the required jacket thickness. The procedure is ob-
tained from theoretical equations based on the geometry shown
in Fig. 1. The resultant forces, Fig. 2, assume the jacket pres-
sure to act uniformly on the outside of the shell over length
L. The half-pipe jacket thickness is assumed small compared
to the thickness of the shell. Hence, forces Qi = Q2 and the
magnitude of each force is obtained from statics as
Q = p'/L/2
From the theory of thin shells (Jawad and Farr, 1989; and
Timoshenko and Woinowsky-Krieger, 1959), the deflection at
any point A, Fig. 3, on the shell due to P', Qu Q2 is given
by
P'R2
2 — e Jxcosjx-e'nL x)
cos j(L-x)
~~ 2Et Fig. 1 Jacketed shell
Qxe~JX
.3 -(sinjx+ cosjx)
-XL-X)
Qie
[smj{L-x) + cosj(L-x)\ (1)
\fD
and the axial bending moment is given by
d2w
M= -D- 2 (2)
dx
The axial membrane stress in the shell due to the half-pipe
jacket pressure is negligible. The axial bending stress can be
expressed as
6D dlw
sb=±-pr=±- t2 dx2
6M
(3)
m*ml r'
The membrane hoop stress is obtained from the expression
Shm=-Ew/R (4)

Contributed by the Pressure Vessels and Piping Division for publication in

the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the PVP
Division, March 31, 1992; revised manuscript received May 11, 1994. Associate
Technical Editor: O. F. Hedden. Fig. 2 Discontinuity forces

3 3 6 / V o l . 116, AUGUST 1994 Transactions of the A S M E

Copyright © 1994 by ASME

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 Q2 Qi

L-X X
^ : 1 ^

Fig. 3 Shell forces

Sh — S),m + Shb

= -(Ew/R)~uS„ (6)
The maximum stress in the shell due to jacket pressure is
obtained by calculating the larger of the two values given by
Eqs. (3) and (6). The maximum stress is obtained by maxi-
mizing the value of w in Eq. (1) for various parameters. These
parameters are E, L, P', R, t, u, and x. Substituting Eq. (1)
into Eqs. (3) and (6) results in an equation that is independent
of the modulus of elasticity E. Hence, E can be discarded from
further consideration. Also, Poisson's ratio, u, can be ap-
30 40 50' 60 70 90 100 110 IdO 130 140 150 160 170
proximated as 0.3 for most half-pipe jacket materials used in
Section VIII-1 construction. Thus, for any given pressure P',
the only variables that need to be considered in maximizing Fig. 4 NPS 4 pipe jacket
the stress are L, R, t, and x. Hence, Eqs. (3) and (6) can be
written as
S„ = P'f(L,R,t,x) L, as a function of R and /. A typical chart given by the ASME
(7)
and Section VIII-1 Code is shown in Fig. 4 for an NPS 4 pipe.
Possible buckling of the shell due to jacket pressure was also
Sh = P'g(L,R,t,x) (8) evaluated for various combinations of L, R, and t. A length
The maximum value of Eqs. (7) and (8) can be expressed as of shell, L, that is less than about 3.12 V # 7 and subjected to
jacket pressure will not buckle due to the staying effect of the
F=P'/K (9) half-pipe jacket. Accordingly, the charts published by ASME
The ASME Subgroup on Design of Section VIII surveyed were limited to a minimum radius of 15 in. to avoid possible
its members and the industry in order to establish practical buckling.
limits for L, R, and t. The survey showed that the most com- Spacing of the half-pipe jackets along the length of the shell
monly used half-pipe jackets in industry are the NPS 2, 3, and varies from vessel to vessel. The effect of spacing two jackets
4 pipes. Thus, the values of L that were considered were 2.375, in close proximity of each other was investigated by writing
3.5, and 4.5 in. Also, it was decided to limit the maximum equations similar to Eq. (1). The results show that the stress
vessel radius, R, to 85 in. and the range of shell thickness, t, is not as large as that obtained from one single jacket, since
between 3/16 and 2 in. the discontinuity force for multiple jackets is spread over a
A computer program was written to calculate the maximum larger length of the shell. Various finite element models were
value of Km Eq. (9) for the given parameters. In the program, run to verify the simplified theoretical solutions. The results
x was incremented from zero to L for specified values of L, indicated that the values obtained from the charts, such as Fig.
R, and t in order to maximize K. The exact location of x that 4, are conservative for closely spaced jackets.
resulted in a maximum K value varied with L, R, and /. The Equation (9) is also applicable to half-pipe jackets in heads.
maximum K value is plotted in a chart for any given pipe size Theoretical equations similar to those of Eq. (1) were checked

Nomenclature

D = £Y 3 /12(l-u 2 )
E = modulus of elasticity P\ = jacket pressure s„ = hoop stress
F = maximum stress in shell P' - permissible jacket pressure Shb = bending hoop stress
/ = variable function Qi = P' L/2 S)im = membrane hoop stress
g = variable function Qi = P' L/2 t = shell thickness
1 =
r = jacket radius T = jacket thickness
4A/3(1-«2)AR¥ R = shell radius u = Poisson's ratio
K = factor S\ = allowable stress in jacket w = deflections
L = size of half-pipe jacket S/, = axial bending stress x = distance

Journal of Pressure Vessel Technology AUGUST 1994, Vol. 116 / 337

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 for spherical configurations. The results show that Eq. (9) can where 0.85 is the joint efficiency factor for the uninspected
be used conservatively in spherical geometries without modi- circumferential butt welds that connect the various segments
fications by using R as the radius of the spherical head. of the half-pipe jacket.
Equation (9) is the main ASME expression for determining Fillet welds are usually adequate to transfer the forces Q
the permissible jacket pressure, P', on the shell. It is used by from the jacket to the shell. For cycle conditions, full pene-
first selecting an allowable stress, F, from the appropriate stress tration welds are recommended to minimize stress concentra-
tables of the ASME Section II-D. The A" value, is then obtained tions.
from the charts similar to that shown in Fig. 4. Equation (9)
is then used to calculate the permissible jacket pressure, P'.
The half-pipe jacket thickness, T, is obtained from the stand- References
ard equation Jawad, M. H., and Farr, J. R., 1989, Structural Analysis and Design of
P*r Process Equipment, John Wiley and Sons, New York, NY.
T=- Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and
0.85 Si-0.6 Pi Shells, McGraw-Hill, New York, NY.

ABSTRACTS OF PAPERS
1994 ASME Pressure Vessels & Piping (PVP) Conference
A diskette that contains a text file of the reference citations
and abstracts for the papers contained in the 1994 ASME PVP
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