Thcrm3J
end reactions
for jacketed
piping
can be pre~icted
carrying
a process
fluid in an inner pipe heated by st8:1m !~
b:.:f',jeen the pipe and jackGt
requires special stress anaiysis: Commonly used to convey very viscous pr~cess fluids in an mner pIpe, neated by steam between the outer jacket ans! inner pipe, thermal end reactions can be predicted. Vaccuum jacketing is also used as an insulator for cryogenic fluicls and can be analyzed using the same calculation method for heated jacketed piping. By example, stress problems occuring with this type of piping system will be descrihed. The example assumes a process fluid requiring const.1nt, uniform heat not available through steam or electrical tracing systems. It further ass,:mcs-the need for a stainless steel Lnner pipe or core and an outer carbon steel pipe or jacket. Since both pipes are rigidly attached to flanges in spool pi.eces and each pire has a difTerent. thermal e~pansion _coefficient, ~xial - str~se~ will be _an_a_ly_·z_e_d_._ JACKETED
/'
An isometric dra\',ing of the sample problem is shown on Fig. 1. The construction is a three inch schedule '10 stainless steel core pipe with a four inch schedu1e ,10 carbon steel jacket. The jacket covers the core for its entire length and flanges arc used for system disrnantlillg. The heating medium is 180 psi-saturated ste<\m; proper collection and removal of condens:lte has been assumed. I t has also been assumed that the core pipe and j:lck~t pipe are at thenn:l! equilibrium. Core/jacket stn:ss anaIJ~si". This ex:tIllple has a process core pres,ure of.3'O'·[?sig";jwith jacket pressure at.J8CJ psig, the.: core is su~ed to an' extern:ll pressurc of 150 psig. The core pipe must be investigated for collapse or local buckling frolll the extemal pressure load, COll\cntional techniques as outlined in the ANSI and AS:\fl~ Coue.:s can be used. Since the core is at the saine temper:lture as t~1<'jacket, in this eX:lI11ple, thr only di!lcn.:utial exp:lnsion would be expcricllccd fn.>lll the uifl""ll:IJ"': in tIll: coefficieJlt of cxpallSi",n hct\\cI'lI t!w st;liJlIt-" eof/.' alld carboJl steel jad:t.:t. The cIJJllpn:ssi\'c :1Il<1 teJlsile stl<>:,('~ Oli b;; teadily
I
Y
/'
/'
~I 0>
n
/'
/'
-PIPING
Example.
I /'/'/'//'/;: J ,(
I
I)
1
I I I
~
I
'
v5pacers
shown as a restraint
i~ I I I I I I I }-
3-in sch. 1055
core pipe
I I
I 1,-4·in, I I
~~~
'" I -(
I I I I
I
I
t4~"
sch,40 C stl jacket
? ±
<~en
._ 6J --:-?}')~
6.\frJ
.~ft~r t~.;__ L'qLi~\'3!f~:1t tLiL~<;. n3s h~~':II c·'" mined: cor:-'LI"i(Jll;-,I flexibility all:llysis tedl! .•iq,..·~, Glil be:
0.2:37:
applied
24,600 psi
±
_ 2( -810) 0.237'
2(-230) 0.237
= 1710 + 27,100
(I 76) (22-' . :J)
_ (1./6t -t-
0
_
(2.2.)
13,550
= +2,360 -15,310
psi outside psi inside
(Radial) = 0 will not be combined with other loadings for the purpose of this analysis, but should always be evaluated. The longitudinal discontinuity stress then becomes:
~3
=
(b) Axial column loading,
=
24,600 psi (Longitudinal Direction) 6,860 psi (Jacket) V
v
Am,
A
m.
e E I
=
J155 psi (Jacket) 2,.QOo.psi, (Assumed) 34,315 psi
K L M. P r.
The difference of combined stresses from (a) to (d), compared to allowables can then be used as a minimum for: (e) thermal external bending loads. In this example Sa = 1.25 (20,000 + 20.,000;---·
== 50,OOOpsi'" Total (a) through (d)=--3"'.f;31S psi (Sl) Allowable t~errnal bending stress (e) 15,685 psi
=
Composite core/jacket analysis. Prediction of terminal end reactions of the composite corel jacket sectioll can be determined by simulating a jacket sheJl thickness that is representative of the combined moments of inertia of the core and the jacket pipe. In our example, the following applies: ~ 3-il1. Scltt 10 Q.2.re,I .:=; 1.82 in4 E =- 28.3 (lOG) 4~i-;-;Scl,lCl Jacket, 1== 7.32 in4 E =- 27.9( IV';) Sidce, for the analysis, we will use the carbon steel jacket with a moclulus of elasticity of 27.9 (lOG), an adjustmclIt in the core moment of inertia would be: I = 1.82 (28.3 127.9) = 1.85 in· Total equi valenl I == 1.85 in' + 7.32 in4 9.17 in4 Using an OJ) of 4.5 inch, the equivalellt shell thickne:;s
r. R
R. .R. S. S. S. S,
t t. !1T.
V. w W
fJ
a a, a. (1
t
~"
=
m; •..· be c:dclJlatcd I
:
9.17 30.2
stres,cs and end re;lc,ifJ!ls.
Step by ste;J approach. :\ reasonable ap?roJ.ch to the: design and ana1ysis of jacketed systems is: 1. Establioh jJ,H,1:nctc'rs f(JI fLl'!:;" and spacer!gu:dcs locations. This is a significant consideration when there is diiferential expansion between the core and jacket. 2. Perform a flexibility analysis of the core pipe when required by the constr-aints of No. I above. 3. Evaluate all combined stresses, i.e. discontir;uit;·, thermal, etc., on an indi\'idual basis. 4. Perform a flexibility analysis, predicting stresses and end reactions, of the combined corel jacket section where inherent flexibility appears to be minimal or strain-sensitive equipment is used. 5. 'Pay special attention to the local effects of vents, pressure taps, drains, etc. for their contrihution to the problem of differential core I jacket expansions. In this example, a computer analysis was perfol1lled for the piping configuratioll shown on Fig. 1. Predicted jacket thennal bending stresse, were within the stn'ss limits estahlished by the analysis of the combined loading,;. \,\'ere this not the case, additional flexibility would be required by geometry changes or a bellows type expansion joint would be provided on the jacket pipe. The bellows would, for practical purposes, eliminate the axial column loading and discontinuity stresses.
PRs t 180(2.25) 0.237
to calculate
A
NOi\IENCLATURE Cross-sectional metal area of the carbon steel jacket. Cross-sectional metal area of the stainless steel core. Constant = 2 for a column with one end fixed and the other free. Modulus of elasticity, psi Momcnt of inertia, in.' Ratio of ring radius to shell radius Unsupported column length 240 m. for a 20 ft. pipe section Momcnt, in.-lbs, Pressure within the jacket = 180 psi Radius of gyration = 1.2 for SS core pipe, in. Equivalent shcll radius, in. Radius of carbon steel jacket, m. Ring radius at 300· F, in. Shell radius, in. Allowable strcss, psi Stress at ambient temperature. = 20,000 psi for example from ANSI B31.3 Stress at operating temperature = 20,000 psi for examplc from ANSI B31.3 Longitudinal strcss, psi Thickncss of the carbon sted pipe, in. Equivalent shell thickncss representing the comhined momenl; uf inertia of the composite corc and jackct Tempcrature difTcrcnce bctwccn avcrage ring tempcrature and ambient, 0 F Shear, Ibs. Width of two pipc flanges, in. Max. or critical load on a structural column, Ibs. Total linear thcrmal exp:wsion betwcen 70 F and tcmperature of st,-alll at 180 psi, in.! I 00 ft. Mcan coefficient of linear thermal cxransion hetwecn 70" F and stealll at 180 l'si. a of carbon steel pipc cOllsiJered as a shcll a of sl"inle>s stecl f1allge cUllsiJercJ as a ringStress, psi Str;lin, in.!in. DifTcrcn,'(" in strain bctWCCll .the core and j:\cket =, [/1 (SS core) - fJ (C st!. jacket)] /1200 whcrc 1200 = lenilth of 100 ft. pipe in inchcs 1.285/V1<.. t
=
0
Sub.
to st'-linll tu c"rholl
S5
steel curc stet'! jacket
L1TrR.\TURE 1 C..-atud.d
tial
and ScbnciJcl-, Rill~ Stifft"nl'rs."
"Sltc:'~l:3
in
a
CITED Pln'.Utl.:
Vt::s~d with
Circuru(r:rcn·
a
